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What is the nature of light? "luminous” (a) Distinguish between and "illuminated” objects. (b) How may objects be rendered luminous? (a) What evidence have we to prove a that vacuum? through travel can light (b) Distinguish between opaque, and sub- transparent translucent stances. Give examples of each. (a) What Is meant by the "rectilinear propagation of light”? Discuss evidence in support of it. (b) Define: ray, beam, converging pencil, diverging pencil. (a) Describe the image obtained in a pin-hole camera. (b) Explain how it is produced. (c) Name three factors that govern its size. (d) The length of a pin-hole camera is 10 in. An object 6ft. high Is placed at a distance of 30 ft. from the pinhole. Calculate the size of the image produced. 6. (a) Define: umbra, penumbra. (b) Construct a labelled diagram to show how both total and partial eclipses of the sun are produced. (a) What is the velocity of light in air? 7. 182 CHAPTER 17 REFLECTION OF LIGHTMIRRORS IV: 9 THE LAWS OF REFLECTION In section IV:2, we learned that most are made visible when light objects falling on them is reflected back to our eyes. The rays of light that fall upon a body are called incident rays, while those that are sent back by the body are called reflected rays. A mirror is a smooth, highly polished surface, designed to reflect a maximum amount of light. Mirrors usually consist of pieces of glass silvered on one surface. Some are flat and are called plane mirrors, while others are called Fig. 17:1 The Optical Disc, for Dem- onstrating the Laws of Optics. 183 Chap. 17 LIGHT curved mirrors. However, any smooth surface, such as polished metal, polished wood, or still water, will serve as a mirror. to the reflecting surface and angles meeting it at the point of incidence is called the normal. Rotate the disc and thus cause the incident ray to strike the mirror at different angles. In each case note the direction of the reflected ray and compare the size of angle of incidence (the angle between the incident ray and the normal), with that of the angle of reflection (the angle between the reflected ray
and the normal). In each case these two angles will be found to be equal, and the incident ray, the reflected ray and the normal will all be found to be in the plane of the disc. Hence we can state the two laws of reflection as follows: First Law: The angle of reflection althe angle of ways equals incidence or Z r = Z i Fig. 17:2 Reflection of Light by a Plane Mirror (a) Using Optical Disc. (b) Terms. Second Law: The incident ray, the normal, and the reflected ray all lie in the same plane. To study reflection of light and other is 17:1). optical phenomena an optical disc This consists of a used (Fig. circular flat disc, graduated in degrees, to which various pieces of optical equipment can be fastened by means of thumb-screws. The disc can be turned about a horizontal axis by means of a handle fastened to the back. Surroundis an opaque collar in ing the which is a window containing one or more horizontal slits. disc Mount a plane mirror at the centre of the disc, with the face of the mirror at right angles to the zero line marked on the disc (Fig. 17:2). Allow a ray of light from a lantern to pass through a single slit in the window of the optical falls upon the mirror. disc so that it Adjust so that the point of incidence coincides with the point where the zero line meets the mirror. This line at right 184 are laws quite These simple and straightforward. We apply them daily in games such as handball, tennis and basketball where the bounce of a ball Experiment 2, chapter 21, is is an alternative method for proving these two laws of reflection. utilized. IV : 10 REGULAR AND DIFFUSE REFLECTION a upon rays fall surface, such as When parallel a smooth reflecting plane mirror, they form the same angle of incidence with the surface, and in consequence they will be reflected as a beam of 17:3a). Such reflection is called regular reflection and often produces undesirable glare. For example, one finds it difficult to read from a glazed paper in parallel (Fig. rays sunlight. Diffuse or irregular reflection occurs REFLECTION OF LIGHT—MIRRORS Sec. IV: 11 when light strikes a rough surface (Fig. 17:3b). Such a surface may be conto be composed of a large sidered number of tiny, flat surfaces that face Thus when parallel in all rays of light strike such
a surface, the directions. individual rays are scattered or diffused due to their being reflected in different directions. To avoid glare it is often necessary to promote diffusion of light. Unglazed paper is used for newspapers, and for Smooth Surface Rough Surface Regular Reflection Irregular Reflection (a) (b) Fig. 17:3 Regular and Diffuse Reflection. Frequently the woodwork wall-papers. in our homes is left with a dull finish. These, and other devices, all cause dif- bulbs, and lamp-shades. Prism light glass and other types of roughened glass in windows serve the same purpose. IV : 1 1 IMAGES IN PLANE MIRRORS Mirrors have many and varied uses. Large plate-glass mirrors are frequently placed on the walls of our homes and of public rooms to give an impression of spaciousness. Rear-view mirrors are now compulsory in all automobiles. Mirrors are often used in scientific instruments to reflect light onto a scale, in projectors to intensify the light beam, in the view-finder of reflex cameras, in periscopes, and the like. In view of such it should be of real widespread uses, interest to us to study the images produced by plane mirrors (Fig. 17:4). On doing experiment 3, chapter 21, you will learn the following facts about images in plane mirrors: The Position of the Image. The image is as far behind the mirror as the object is in front, and a line joining the two right the passes through mirror at fuse reflection of light. angles. Diffusion, and hence the elimination of glare, is also obtained by transmission of light through frosted or opalescent The Characteristics of the Image. The image is the same size as the object. it only It is a virtual image, that is, Fig. 17:4 Images in a Plane Mirror (a) The Position and Characteristics of the Image. (b) Lateral Inversion. 185 Chap. 17 LIGHT appears to be there. No light emanates from it. Such an image cannot be proThe image is jected onto a screen. vertically erect, but laterally inverted. When we say “laterally.inverted” we mean that the right and left sides are interchanged (Fig. 17:4b). Note that when the mirror is horizontal, the image is vertically as well as laterally inverted. Recall what you observe on looking into a still body of water to verify this fact
. IV: 12 TO LOCATE IMAGES IN PLANE MIRRORS These phenomena observed experimentally can be shown to be true as a geometrical consequence of the laws of reflection, Sec. IV; 9. Let us consider the simplest possible case, that of a point object, O, the image of which, I, is viewed by an eye BD (Fig. 17:5). O is sending out light rays in all directions. Point in a Plane Mirror. lying between OAB and Only those OCD enter the pupil of the eye after being reflected from the mirror. The reflected rays AB and CD appear to be 186 coming from I, their point of inter- section. In order to locate the image of an object in a plane mirror geometrically, the following construction is necessary (Fig. 17:6). From each point of the to object, draw a perpendicular the mirror, and extend it an equal distance behind the mirror. Join the ends of all such lines and you will have an outline of the image of the object. Using the half arrow ( j ) enables you to indicate lateral inversion nicely. To show how the eye sees the image place a diagram of an eye on the same side of the mirror as the object. Draw a cone of rays from the tip of the image to just fill the pupil of the eye. Draw two light rays from the tip of the object to the two points on the mirror where the previous rays met the mirror. Put arrows on the Repeat this real light rays as shown. same procedure for each point on the object. Thus the eye is receiving light that appears to originate from the virtual image behind the mirror, but actually comes from the object. In all diagrams, use faint lines for construction, dotted lines for imaginary rays or virtual image, and solid lines for real rays, real image, object, etc.. REFLECTION OF LIGHT—MIRRORS Sec. IV: 13 Fig. 17:7 Images in Parallel Mirrors. IV: 13 PLANE MIRROR SYSTEMS 1. Parallel Mirrors On looking into a mirror facing a parallel mirror on the opposite wall of a room, such as is used in barber shops, a very large number of images of the room can be seen stretching away almost endlessly. To discover how these are formed study Fig. 17:7 carefully. {ii, 12, h) A series of images representing the side of O facing mirror Mi are formed (/i, 1 2, 1.3,) and
also a series of images representing the side of O facing mirror These multiple images '^^2 are due to the image formed in one mirror, acting as the object, which in turn forms an image in the second mirror, and so is absorbed at each reflection, each succeeding image is fainter than the one preceding. Since some light on. 2. Mirrors at Right Angles When two mirrors are placed at right angles to each other (Chap. 21, Exp. 4), three images of an object will be 17:8). Ii and h are observed images of O in mirrors Mi and M^. the mirror is the image of Ii (Fig. in Is M 2 produced (Mg produced is really an image of M 2 in Mi) and of I 2 in mirror Mi produced, these two images coinciding. How the these eye sees 1 3. Fig. 17:8 Images in Mirrors at Right Angles. images may be shown by a construction similar to that used previously. Mirrors Inclined at Sixty Degrees When mirrors are inclined, the number of images obtained depends upon the 187 Chap. 17 LIGHT angle between the mirrors. we can say: In general the number of images _ 360 ^ Z Inclination For example, using angles we obtained three images mirrors at If two mirrors are inclined at 60°, five images will be obtained 17:9). (Fig. right IV : 14 CURVED MIRRORS These form multiple images of differently shaped pieces of coloured glass placed between them. Many beautiful and fascinating designs can be produced at every turn of the instrument. Curved mirrors are frequently more suitable than plane mirrors for certain purposes. Curved mirrors are used as rear-vision mirrors, as shaving mirrors and as reflectors for car headlights. One important type of curved mirror is the spherical mirror whose reflecting surface is a portion of the surface of a sphere. If the inner surface is the reflecting surface, it is a concave mirror; if reflection occurs at the outer surface it is a convex mirror. We represent such mirrors in cross-section by the arc of a circle (Fig. 17:10). Silvered Surface Reflecting Surface Silvered Surface Reflecting Surface Fig. 17:9 Images in Mirrors inclined at 60°. Sir David Brewster, of Edinburgh, making use of the images produced by inclined mirrors, in 1819 invented the kaleidoscope. This consists of three mirrors set at angles of 60° to each other. Spherical Mir
rors. Fig. 17:10 (a) Concave or Converging. (b) Convex or Diverging. A few terms used in connection with curved mirrors need to be defined (Fig. 17:11): 188 REFLECTION OF LIGHT—MIRRORS Sec. IV: 14 Fig. 17:12 Action of Curved Mirrors. (A) Concave. (B) Convex. Centre of Curvature, C, is the centre of the imaginary sphere from which the mirror was cut. that is, points through which reflected However, light rays are converged. there is only one principal focus as Vertex, F, is the mid point of the mir- defined. ror. Principal Axis, PV, is the line through the centre of curvature and the vertex of the mirror. Secondary Axis, CD, is any other line drawn through the centre of curvature to the mirror. Since all radii of a circle meet the circumference at right angles, and since all axes behave like radii since they pass through the centre of curvature, it follows, that a Normal to the surface of a curved mirror at the point of incidence is simply a secondary axis. to it) pass, close Principal Focus, F, is the point on the principal axis, through which rays, travelling parallel to the principal axis (and fairly after being reflected from the mirror. For a convex mirror, the principal focus is a virtual focus, and is that point from which such rays appear to diverge after reflection from the mirThis point will be found to be ror. midway between the centre of curvature and the vertex of the mirror. There are many other foci possible. Focal Length, FV, is the distance from the principal focus to the vertex of the mirror. The action of curved mirrors (Chap. 21, Exp. 5), may be demonstrated by means of the optical disc. Mount a concave mirror on the optical disc so that the 0°—0° line becomes the prin- cipal axis of the mirror. Insert a metal shield with several parallel slits in the window of the opaque collar and shine light from a projection lantern through these slits onto the mirror (Fig. 17:12). You will note that the reflected rays conIf the disc is rotated so that the verge. incident rays are parallel to the principal axis it will be found that the reflected rays converge through a point. This point is the principal focus of the mirror.
Similarly, if we insert a convex mirror in place of the concave one, and repeat the above, it will be found that the reflected rays diverge as though coming from a point behind the mirror. This virtual point locates the principal focus of the convex mirror. 189 Chap. 17 LIGHT IV: 15 IMAGES IN A CONCAVE MIRROR In chapter experiment 21 we 6, studied the characteristics and position of images formed by a concave mirror for difTerent positions of the object. As the object was moved closer to the mirthe image, which was real and ror, Rays Used to Locate the Fig. 17:13 Image, I, of an Object, O, in a Concave Mirror. inverted, gradually grew larger in size and moved farther from the mirror. When the object was located inside the principal focus of the mirror, the image became virtual and erect and was located behind the mirror. All of these results can be verified with fair accuracy by means of simple geometric diagrams. The principles used here are very similar to those used previously with plane mirrors. Each point on the object is sending out rays of light in straight lines in all directions. If we trace the paths of several of these rays from a point on the object, to the mirror, and then their rays back from the mirror, we will find that they intersect. The point of intersection is the point on the image that corresponds to the original point on the object from whence the light rays came. reflected Suitable rays for this purpose, as illustrated in Fig. 17:13, are: 190 1. A ray from the object parallel to the principal axis, which will be reflected through the principal focus. 2. A ray from the object through the centre of curvature which will be reflected back along the same path, since the incident ray strikes the mirror at right angles. 3. A ray from the object through the principal focus, which will be reflected parallel to the principal axis. 4. A ray from the object to the vertex of the mirror, which will be reflected so that the angle of incidence equals the angle of reflection. 5. Any other ray from the object to the mirror will be reflected so that Z f = Z r. In actual practice any two of these rays will suffice. The first two mentioned are the most easily drawn and hence are the most convenient to use. In order to verify the observations obtained in our experiment, it is necessary to make accurate scale drawings. To Locate the Image in a
Fig. 17:14 Concave Mirror of an Object Placed Beyond F. For example, if the focal length of the concave mirror was 20 cm., the object 60 cm. from the mirror, and 12 cm. high, our construction would be as above (Fig. 17:14), using the scale 10 cm. = 1 cm. REFLECTION OF LIGHT—MIRRORS Sec. IV; 17 Draw principal axis, PV. With centre C, and radius of curvature 4 cm. (twice focal length), draw an arc to represent the mirror. Locate the principal focus F, midway between C and V (2 cm. from mirror). Locate the object O, 6 cm. from the mirror. Draw the object (OOi) 1.2 cm. high and perpendicular to the axis. From the tip of the object (Oi) draw the two rays and their reflected rays as outlined on previous page. These rays intersect at /i, and hence locate the position of the tip of the (Rays from other points on the image. would corresponding object image points. sufficient.) Draw the image 11 1, perpendicular to PV. The distance of the image from the mirror and its size can be obtained by measuring accurately. Notice that when the object is beyond the image is between F and C, C, real, smaller than the object, and inverted. See how perfectly this diagram confirms your observations recorded in the table on page 242. produce However, one the is To Locate the Image in a Fig. 17:15 Concave Mirror of an Object Placed Between F and V. of for other positions The student should construct similar diagrams the object, and verify the other observations made. The special case, where a virtual image is obtained, is slightly more difficult. Study the following diagram carefully, and note the method is that identical to that given previously (Fig. 17:15). However, this time the reflected rays diverge, and therefore appear to come from a point behind the mirror, thereby creating the virtual image. IV : 16 IMAGES IN A CONVEX MIRROR One has often observed the images produced by the back of a spoon, the side of a tea-kettle or the shiny fender of a car. Such objects as these are all acting as convex mirrors. In experiment Fig. 17:16 To Locate the Image in a Convex Mirror. 7, chapter 21, we found that the images in a convex mirror were always
behind virtual, smaller than the the mirror, object, and erect. The same method is used as with the concave mirror to verify this geometrically (Fig. 17:16). IV: 17 HOW THE EYE SEES THE IMAGE discussed As previously section IV: 12, the eye sees the image by means of rays which actually come from the object, but which appear to come from in Fig. 17:17 How the Eye Sees a Real Image in a Concave Mirror. 191 Chap. 17 LIGHT : the image. Fig. 17:17 and 17:18 show how this is accomplished. In each case the light rays start from the object, are reflected at the mirror, pass through a real image or appear to come from a Fig. 17:18 How the Eye Sees a Virtual Image In a Convex Mirror. virtual image, and enter the eye. In order to construct these diagrams just reverse the previous order. That is, join 7 to the outer edges of the pupil of the eye. This cone is projected back to the mirror or cuts the mirror. From there it is drawn back to the object.!V: 18 THE MIRROR FORMULAE In the previous sections we have been studying the images produced by curved It is possible by means of two mirrors. simple formulae to determine the location and characteristics of the image for various positions of the object. To do a consistent convention regarding so, signs must be followed. Values for distances of objects and real images are always positive; those for virtual images are negative. Similarly, the focal length of a concave mirror (which has a real is positive, that of a principal focus) convex mirror (with a virtual principal is negative. To state this confocus) cisely, the convention of signs is: “real is positive, virtual is negative” The two formulae, with worked examples to show how to use them, follow (a) Magnification Formula Height of Image Distance of Image Height of Object Distance of Object 77o Do Note the similarity of this formula with that obtained for the pin-hole camera (Sec. IV: 4). (b) Distance Formula Distance of Object Distance of Image _ 1 Focal Length 1. An object 2 in. tall is placed 15 in. from a concave mirror whose focal length is 5 in. Find the position and size of the image. Examples Ho= 2 in. Do = 15 in. f = 5 in. Di=? 1 1
_ 1 — + Do Dr 7 — + 1 1 1 T 1 15 15 1 _ 1 D,“ 5 :.2Di — 15 :.Di =7.5 The image is located 7.5 in. from the mirror. 192 Ho— 2 in. Do = 15 in. Dj — 7.5 in. REFLECTION OF LIGHT—MIRRORS. Hi ^ A ‘ Ho~ Do. Hi _ 7.5 ~ 15'2?. ‘ Sec. IV: 19 The image is 1 in. tall. Check these results by making an accurate scale construction to locate the image geometrically. Both position and size of image should agree closely with the above values obtained by calculation. 2. An object 5 cm. high is placed 30 cm. from a convex mirror whose focal length is 20 cm. Find the position, size, and nature of the image. Ho= 5 cm. Do = 30 cm. f = — 20 cm. Di =?'Do^ Di f 30 1 _ ~~ ‘ Di. ‘ Di — 20 1 1 20 30 _ -3 -2 ” 60 — 5Di=:60 Di = — 12 cm. Image is 12 cm. from mirror and is virtual (since sign is negative). Ho= 5 cm. Do = 30 cm. 12 cm. Di? ‘ Ho Do ‘ ’ 5 ~ 30 Hi = 2 cm. Image is 2 cm. high. IV: 19 APPLICATIONS OF MIRRORS Reference has already been made in section IV : 1 1 to the uses of plane mirrors. Many of these uses, however, are more satisfactorily fulfilled by using curved mirrors. For example, a plane mirror is frequently used as a shaving mirror. However, a concave mirror so used produces an enlarged erect image when the face is held between the principal focus and the vertex of the mirThe enlarged image is often a ror. Similarly, a convex distinct advantage. mirror is frequently used as a rear vision mirror instead of a plane mirror. The erect, smaller image produced gives a wider field of view with the same size mirror. Spherical mirrors such as we have been describing have one serious defect, known as spherical aberration. In such mirrors, only those rays parallel to the principal axis and fairly near to it pass through the principal focus on being 193 Chap. 17 LIGHT are axis (Fig. 17:19). reflected from the mirror. Rays farther from the principal
reflected through points some distance from the Conversely, if a focus source of light is placed at the principal focus, the reflected rays will not form a parallel beam, but the outer ones will be scattered and hence the light is weakened. Fig. 17:19 Spherical Aberration in Curved Mirrors. To overcome this parabolic rather than spherical mirrors are used defect, 17:20). A parabola is a section (Fig. from a cone obtained by cutting the cone Fig. 17:20 A Parabolic Mirror Used to Prevent Spherical Aberration. by a plane parallel to a line from the apex of the cone to any point on the circumference of the circular base. All rays which emanate from the principal focus of such a mirror, after reflection are parallel to the principal axis, no matter how great the aperture is. As a result parabolic mirrors are used as reflectors for searchlights, car headlights and in the reflecting telescope. IV : 20 QUESTIONS A 1. (a) Define: angle of incidence, angle of reflection. (b) State the two laws of reflection and indicate how you could test them. 5. 2. (a) Distinguish between diffuse and locate the image of an inclined arrow in a plane mirror. (b) Show how an eye sees the image. (a) How many images will be observed in 2 mirrors inclined at 45°? (b) Draw a diagram to locate these images. glare de- 6. (a) Define: principal axis, principal regular reflection. (b) How is undesirable creased? 3. (a) State the rule for determining the position of an image in a plane mirror. (b) Describe the Image. between (c) Distinguish real and virtual images. (a) Show by a diagram how you can 4. 194 focus, focal length. (b) By means of accurate construction show how the of (i) a concave mirror, and (ii) a convex mirror may be located. principal focus 7. (a) Under what conditions does a concave mirror form (i) a real image, (ii) a virtual image? REFLECTION OF LIGHT-MIRRORS Sec. IV: 20 (b) Describe the size and location of all the real images produced by a concave mirror. (c) When a concave mirror is used in shaving, where is the person’s face in relation to the principal focus of the mirror
? What kind of image is seen? 8. An object is located just beyond the centre of curvature of a concave mirror. (a) By means of a diagram locate its image. (b) Show how the eye sees the image. (c) State the characteristics of the image. 9. (a) State uses of plane, concave and convex mirrors. (b) How does a searchlight produce a narrow beam of light? B 1. A watch seen in a mirror seems to read (a) 2 o’clock, (b) 6.15 o’clock. What does it actually read? Explain. 2. Support a mirror vertically on a desk and stand a book in front of it to serve as a screen. Draw a triangle on a piece of paper and lay it flat between the book and the mirror. Watching the image in the mirror, but not the triangle itself, try to retrace the triangle. Why do you have difficulty? 3. What changes would you observe in your image as you walked toward (a) a plane mirror, (b) a concave mirror, (c) a convex mirror? the position grams locate of the image for each position of the object, (b) State the characteristics of each image. accurate 5. By means of an scale diagram locate the image produced by a convex mirror, whose focal length is 15 in., of an object 6 in. high and 2 ft. distant. State the characteristics of the image. 6. An object is 4 in. tall and its image is 6 in. tall when the object is placed 2 ft. from the mirror. How far is the image from the mirror? 7. A 6 in. pencil is ft. in front of a curved mirror. Find the length of the image if it is 8 in. from the mirror. 1 8. How tall is an object if it produces an image 3 in. tall located 7 in. behind a convex mirror when the object is located 1 0 ft. in front of the mirror? 9. An object 4 in. in front of a concave mirror produces an image 1 2 in. behind the mirror. Find the focal length of the mirror. 10. An object is 1 8 cm. in front of a concave mirror which has a focal length of 1 2 cm. How far is the image from the mirror? 11. An object 9 in. from a convex mirror produces an image 3 in. behind the mirror. Find
the focal length of the mirror. 12. An object is 15 cm. from a convex mirror of focal length 20 cm. Calculate the image distance. 4. An object 15 cm. high is located (i) 75 cm. (ii) 60 cm. (iii) 45 cm. (iv) 30 cm. (v) 20 cm. from a concave mirror whose focal length is 30 cm. 13. The focal length of a concave mirror is 12 in. How tall is the image of a 5 in. candle standing 15 in. from the mirror? 14. Repeat question 13 using a convex (a) By means of accurate scale dia- instead of a concave mirror. 195 CHAPTER 18 REFRACTION OF LIGHTLENSES phate (hypo) and a few drops of hydrochloric acid. These materials will render the water slightly turbid and make Incident Mirror Refraction of Light on PassFig. 18:2 ing from Air to Water or from Water to Air. visible a light beam projected through Shine a beam obliquely upon the it. surface of the water (Fig. 18:2). Part of this beam will be reflected at the surface of the water, and part will be If a refracted as it enters the water. normal (perpendicular) is placed at the point of incidence, it will be observed that the light beam is bent toward the normal. Similarly, if we shine the beam of light obliquely up through the water and into the air, it will be observed to bend away from the normal. Both effects can be shown simultaneously by placing a plane mirror on the bottom of the tank Note that no refraction (Fig. occurs if the light enters or leaves the water at right angles to the surface. 18:2). We may also show that a beam of light is refracted on passing obliquely IV; 21 MEANING OF REFRACTION Water frequently appears to be much shallower than it actually is. An oar or stick when only partly submerged appears to be bent upwards at the surface of the water (Fig. 18:1). These phenomena, and many others similar to them, are due to the bending of light rays as they pass obliquely from one medium into another of different optical Fig. 18:1 Partly Immersed Stick Ap- pears Bent. density (Sec. IV: 22). Such bending of the light rays is called refraction. Refraction of light as it passes from air
into water, or from water into air, can be illustrated Fill a tank with water containing a small amount of fluorescein, or a little sodium thiosul- easily. 196 REFRACTION OF LIGHT-LENSES Sec. IV: 23 from air into glass, or from glass into Place a semicircular block of glass air. on the optical disc, so that its flat edge is bisected at right angles by the 0°-0° Shine a ray axis of the optical disc. of light so that it strikes the surface at this central point where the axis crosses it. The axis thus is made the normal to the refracting surface. The light will Fig. 18:3 Refraction of Light on Pass- ing from Air to Glass. be refracted as shown in Fig. 18:3. Why is the light not refracted on leaving, or on entering the circular surface of the glass? From the preceding observations we may summarize the behaviour of light rays in passing from one medium into another of different optical density, as follows: 1. When a ray of light passes obliquely from one medium into another of greater optical density, it is refracted toward the normal. 2. When a ray of light passes obliquely from one medium into another of less optical density, it is refracted away from the normal. It follows from the above that when a ray of light enters a new medium at right angles to the surface, no refraction occurs. IV: 22 EXPLANATION OF REFRACTION We may ask what causes refraction of light. The following illustration should help us to understand it. Suppose the brakes of an automobile are improperly adjusted, those on the right wheels holding better than those on the left. When the brakes are applied, the car will swerve to the right, that is, to the side that is slowed up most. Similarly, the bending of the light beam, or refraction, is caused by the change in the velocity of light as it passes from one medium into another of different optical density. The greater the optical density of a substance the more slowly light will travel through it. According to the wave theory, light travels out from the source as spherical waves. When a wave-front enters an optically denser medium obliquely (Fig. 18:4), that part of it that enters the new medium first will be slowed, while the rest of it continues to advance at the same speed as before. Consequently, the wave-front swerves
toward the normal as it enters the denser medium. Conversely, the wave-front would swerve away from the normal as it speeds up on passing into an optically less dense medium. No bending occurs if the light enters the new medium at right angles to the surface, for the entire wave-front would be slowed down or speeded up at the same instant. IV : 23 INDEX OF REFRACTION From Fig. 18:4 it is evident that the light is travelling the distance PR in one medium (air), while it travels the distance OQ in the other medium. Hence these distances must be proportional to 197 Chap. 18 LIGHT the velocities of the light in the two media. Also, it should be evident that the amount of refraction is governed by these In the study of refraction only acute angles are involved. When the angle is contained in a right-angled triangle, its sine is a constant quantity found by dividing the length of the side opposite A the angle by the length of the hypotenuse. For example, in A ABC, Fig. 18:4 Refraction of Wave Front on Entering an Optically Denser Medium. relative distances or these relative velocities, and would be constant for any two given media. This ratio is called the index of refraction, and may be defined as follows: Index of Refraction of a medium (yu,) Velocity of light in air Velocity of light in the medium V (air) V (medium) and AB Sin Z ACB = Sin Z CAB = — AC BC AC To prove that: Index of Refraction (u) = Sin Z i Sin Ir PR OQ PR OQ V (air) ^ Sin Z i V {medium) PR/ OR Sin Ir OQ/OR P ~ Sin Z i TZ Sin Z ^ In experiment 8, chapter 21, by means of a simple geometric construction it shown that Index of Refraction is Sine of angle of incidence Sine of angle of refraction The sine of an angle ( abbreviated sin Z ) is a property of an angle found useful in calculations in mathematics and science. The index of refraction is an important physical property of a transparent medium. An instrument, called a refractometer is used to measure' its value quickly and accurately. This enables scientists to identify substances and to If the index of recheck their purity. fraction of a substance is known the velocity of light may be determined for that substance. A substance with a large
index of refraction is said to have a REFRACTION OF LIGHT-LENSES Sec. IV: 25 high optical density, because it permits light to travel through it at a relatively Such substances refract slow velocity. light to a greater extent than do those with a smaller index of refraction. The brilliance of diamonds, and other precious stones is largely due to this fact (Sec. IV: 26). The index of refraction of a substance varies with the colour of the light that passes through it. The rainbow and the beautiful colours obtained when light is refracted through cut glass and precious stones are due to Temperature, too, this has an effect on the index of refraction because it alters the optical density of The waviness observed a when light rising above a hot object is caused by the differing.refractive indices of various layers of hot and cold air. passes through air (Sec. IV: 37). substance. The Index of Refraction of Some Common Substances W ater Crown Glass Flint Glass 1.3 1.5 1.7 Quartz Zircon Diamond 1.5 1.9 2.4 IV : 24 REFRACTION THROUGH A GLASS PLATE When a ray of light passes obliquely through a glass plate with parallel sides (Chap. 21, Exp. 9), it is refracted both on entering and on leaving the glass. On entering, the light is slowed down and Fig. 18:5 Refraction Through a Glass Plate with Parallel Sides. is, therefore, refracted toward the normal. On emerging, speeds up again, and hence is refracted away from the normal. Since this second effect exactly counteracts the first the speeding up exactly compensates for the light the (i.e., Fig. 18:6 Why an Object Appears 'Closer When Viewed Through a Glass Plate. original slowing down), the emergent ray will be parallel to the incident ray but laterally displaced (Fig. 18:5). The amount of this lateral displacement depends on the refractive index of the glass, on the angle of incidence, and on the thickness of the glass. On looking' at an object through such a plate, it will be slightly displaced in position and will appear nearer to the eye than it is in fact (Fig. 18:6). The same thing occurs in water and this accounts for the diffi-culty in locating the exact position of an immersed object (Chap. 21, Exp. 10). IV: 25 REFRACTION
THROUGH PRISMS A prism consists of a wedge-shaped portion of a refracting substance, bounded by two plane surfaces inclined at an angle to each other, this angle being called the refracting angle. When a ray of light enters such a prism it is slowed down, and therefore refracted toward the normal. On leaving, it speeds up, and therefore bends away from the normal. This can be shown by mounting a 60° prism on an optical disc and shining a ray of monochromatic light, e.g., red, through it. From Fig. 18:7 it is seen 199. Chap. 18 LIGHT that both these refractions are toward the thick base of the prism. Hence the light is bent, or deviated, quite consid- A prism when the refracted ray passes through the prism parallel to the base. Finally, the amount of deviation depends upon the colour, or the wavelength, of the light used, which is why monochromatic light was used in these experiments. gives prisms one of their large areas of usefulness. More discussion on this follows in the chapter on colour, page 213. factor This latter Fig. 18:7 Deviation Through a Glass Prism. erably from its original path. The angle of deviation, D, is obtained by extending the incident and emergent rays to meet (Chap. 21, Exp. 11 ) The amount of deviation produced by a prism depends upon a number of facFirst, the material comprising the tors. prism—^the greater its index of refrac- tion, the greater will be the deviation produced. Secondly, the shape of the prism—^^the greater its refracting angle, the greater will be the angle of deviation. Thirdly, the angle of incidence at which the light meets the prism. This can be shown by rotating the optical disc and observing the amount of deviation for various angles of incidence. Minimum deviation is obtained from an equilateral IV : 26 TOTAL REFLECTION It is more usual to consider light passing from air into an optically denser medium; however, when it goes from the optically denser medium into air, or a less dense medium such as from water or glass into air, a peculiar phenomenon occurs. As the light speeds up on entering the air obliquely it bends away from the normal. As the angle of in the denser medium inincidence creases, we finally come to a position when the refracted ray just grazes the surface
, that is, the angle of refraction equals 90°. This angle of incidence is angle. When the called the critical incident angle exceeds the critical angle the light is completely reflected, a phenomenon known as total reflection (Fig. 18:8). Using the semicircular block of glass on the optical disc as in section IV:21, shine a ray of light through it. Rotate the disc to increase the angle of Fig. 18:8 Total Reflection of Light (a) On Passing from Water to Air. (b) On Passing from Glass to Air. 200 REFRACTION OF LIGHT—LENSES Sec. IV: 26 incidence and note the size when total This angle, the reflection first occurs. critical angle for glass, is about 42°. Fig, 18:9 An Illustration of Total Reflection. V An example of total reflection is seen when an empty test-tube is placed in a Canadian Industries Ltd. An Interesting Example of Light Being ''Bent" in a "Perspex" Rod. beaker of water (Fig. 18:9). On looking down into the water the sides of Applications of Total ReFig. 18:10 flection Prisms (a) A Simple Periscope. (b) Field Glasses. 201 Chap. 18 LIGHT, is very Total reflection test-tube appear silvery. This is the due to the light striking the surface of the tube at an angle greater than the This light is critical angle for glass. totally reflected to the eye as shown. Similarly a sooted ball appears silvery on being lowered into a beaker of water. A layer of air entrapped by the coating of soot produces a water-air -boundary at which reflection occurs. a useful phenomenon. Total reflection prisms are usually right-angled prisms with wellpolished faces. Light enters such a prism at an angle of incidence of 45°, which is greater than the critical angle for glass (p. 201), and hence total reflection occurs. Such prisms are used in periscopes (Fig. 18:10a), range finders, field-glasses (Fig, 18:10b), and reflecting telescopes. They are much more efficient reflectors than mirrors, since mirrors reflect only about seventy per cent of the light they receive, whereas prisms reflect a much greater proportion. In addition, prisms are more robust, there is no silvering to tarnish and they give rise to a single well-defined image. The
brilliancy of diamonds, brilliants, and cut-glass dishes is due to total reflection. The greater the index of refraction of a substance the smaller is its critical angle. Diamonds have a large index of refraction (Sec. IV: 23) and consequently have a small critical angle. The surfaces of the diamonds meet each other at such angles that much of the light entering a diamond is totally reflected a number of times internally, before eventually being refracted out. This lights up many surfaces, and gives the diamond its sparkle. Brilliants, and cut-glass articles are often made of leaded The addition of lead increases the index of refraction, and consequently the cut faces are able to cause much total reflection. glass. 202 IV : 27 ATMOSPHERIC REFRACTION Light travels faster in a vacuum than in air. Therefore, light reaching us from the sun and stars will slow up and be refracted as it enters the atmosphere of the earth. Since the atmosphere gradually becomes denser as the altitude decreases, the light will be refracted more and more as it passes through successive layers of denser air nearer the surface. Consequently, when light comes to us obliquely from the sun and stars these S' A' Fig. 18:11 Atmospheric Refraction (a) The Sun Low on the Horizon. (b) A Mirage. the distances increased bright objects appear higher than they really are (Fig. 18:11a). This effect is most pronounced at low altitudes because of the larger angles of incidence, and be travelled through the successive layers of air. As a result the sun appears to set several minutes after it has actually passed below the horizon. The enlarged and sometimes elliptical appearance of the sun and moon when near the horizon is due to the fact that rays from the to REFRACTION OF LIGHT—LENSES Sec. IV: 28 lower edge are refracted more than those from the upper edge. A mirage is a well-known optical illusion caused by refraction and sometimes total reflection of light as it passes through layers of atmosphere of varying density (Fig. 18:11b). Objects in the distance may be raised above or depressed below their normal position and may be distorted into irregular fantastic shapes. The most commonly observed mirage is that of an apparent layer of water over a hot level sandy surface, or paved roadway. The mirage in these cases sky, produced by total reflection from layers of air near the ground. really an image of the is IV: 28
LENSES A lens is a piece of transparent refracting medium, usually glass, bounded by two spherical surfaces, or by a plane and a spherical surface. There are two main types: (a) Converging or Convex Lenses are thicker at the centre than at the outer edge. Such lenses always refract rays of light so as to converge them. They therefore collect light. CONVERGING or CONVEX DIVERGING or CONCAVE Fig. 18:12 Kinds of Lenses. (b) Diverging or Concave Lenses are thinner at the centre than at the These lenses cause outer edge. They to diverge. light rays therefore scatter light. Fig. 18:13 Comparison of Lenses and Prisms, (a) Action of a Converging Lens. (b) Action of a Diverging Lens. 203 Chap. 18 LIGHT These two types of lenses may be of varying shapes as shown in Fig. 18:12. Each shape is devised for a specific purpose. The action of a lens is similar to that o-f two prisms base to base (Fig. 18:13). As discussed in section IV: 25, the light is bent toward the base of the prism both on entering and leaving the prism. Similarly, the light is bent toward the thicker part of the lens both on entering and leaving it. These examples explain the converging action of a convex lens, and the diverging action of a concave lens. Fig. 18:14 Terms Pertaining to Lenses. The study of lenses makes use of a new vocabulary. The terms used are explained below (Fig. 18:14) : Centre of Curvature C, In most lenses there are two centres of curvature. They are the centres of the spherical surfaces that bound the lens. Principal Axis of a lens is the line passing through the centres of curvature of the two faces, or, in the case of a lens which has one face plane, it is the line passing through the centre of the curved face and curvature of which is normal to the plane face. Optical Centre O, is the point on the principal axis midway between the two surfaces of the lens. All distances along the principal axis are measured from this point. Principal Focus F, of a convex lens is that point on the principal axis to which a beam of light which is parallel to the principal axis converges 204 after refraction through the lens. (In a concave lens, the principal
focus is a virtual point, and is that point on the principal axis from which a beam of light, which is parallel to the prindiverge on cipal being refracted through the lens.) axis, appears to Focal Plane is a surface that passes through the principal focus perpendicular to the principal axis of the lens. Focal Length is the distance of the principal focus from the optical centre of the lens. Note 1: In Fig. 18:15 (see below) a line has been drawn through the optical centre of the lens perpendicular to the principal axis. For simplicity, we may represent the entire refraction of light as occurring at this line. Actually, of course, a light ray will be refracted both Fig. 18:15 Represented and Actual Paths of Light Through a Lens. on entering and on leaving the lens. This actual path of the light through is shown by drawing a line the lens between the point where the incident ray enters the lens, and the point where the refracted ray leaves the lens. Note 2: A ray through the optical centre of a lens may be considered as passing straight through the lens. This lens is through which the light is travelling are almost parallel. Therefore, the light will be refracted on entering and on leaving because surfaces the the of REFRACTION OF LIGHT—LENSES Sec. IV: 29 in such a way that the emergent ray will be parallel to, but laterally displaced from, the incident ray (Sec. IV: 24). We shall consider all our lenses to be very thin, so that the amount of lateral displacement is negligible. Increasing either or both of these increases -.the amount of bending of the light and so shortens the focal length. The powers of lenses used in most optical instruments are usually expressed in terms of their focal lengths. IV: 29 FOCAL LENGTH OF LENSES To determine the focal length of a lens the position of the principal focus In optometry it is more usual to deal with the power of a lens rather than its focal length. The unit of power is the dioptre, which is the power of a converging lens of focal length one metre (100 centimetres). The shorter the focal the greater the power of the length, lens, and accordingly the power can be the focal related length the by to formula: r,, P (dioptres) X 100 / (cm.) According to our convention of signs (Sec. IV: 18, and IV: 32), a conve
x lens with a real principal focus has a positive focal length and a 4- power; a concave lens with a virtual principal focus has a negative focal length and a — power. If a lens is used in a different medium, its focal length and therefore its power will change. This can be shown by placing a lens in a tank of turbid water (Fig. 18:17). Shine a parallel beam of Comparison of Focal Lengths Fig. 18:17 of Lens (a) In Air (b) Immersed in Water. 205 Concave Fig. 18:16 Principal Focus of a Convex Lens and a Concave Lens must first be determined and then its distance from the optical centre of the lens measured (Chap. 21, Exp. 12). This may be demonstrated by placing a convex lens on an optical disc. Shine a number of rays, parallel to the principal axis, through the disc and note the point through which they converge. This point is the principal focus (Fig. 18:16). The focal length depends upon the index of refraction of the lens and its thickness. Chap. 18 LIGHT : For example, a glass globe of water in sunlight could focus the sun’s rays. If flammable material should be located at the principal focus of this lens a fire could easily result. Use is made of this very fact in some types of sunlight recorders used by weather bureaus. A sunlight recorder is a device used to determine the number of hours of bright sunshine. In Ontario, the meteorological department uses Campbell-Stokes Sunshine Recorder consists essentially of two parts 18:18). (Fig. the It ( 1 ) A glass sphere which brings the sun’s rays to a focus. (2) An approximately spherical metal light through the water and the lens, and compare the focal length in water with that previously obtained in air. It will be found to be longer. This is to be expected as there is a smaller decrease in velocity of the light going from water to glass than when going from air to glass. Consequently there is less bending of the light, and therefore a longer focal length. A convex air lens in water would function as a diverging lens. ExIt can be constructed by plain why. cementing watch glasses together using a waterproof cement. Care should be observed in the use and location of spherical transparent objects. 206 ; REFRACTION OF LIGHT—LENSES Sec. IV: 31 bowl carries cards which form a belt
on which the sun burns a record. lens. This ray may be considered straight through the as lens (Sec. IV; 28). passing recorder. Real care must be observed in setting up There must be no obthe structions that would shield the recorder It must be placed from the sun’s rays. table, and made perfectly on a rigid Instructions are always provided level. for adjusting for latitude, and for adjusting for the time meridian. The glass ball must be kept perfectly clean at all times. IV: 30 IMAGES IN CONVEX LENSES Previously we saw how images were ( Sec. IV formed in concave mirrors 15). Convex lenses form a very similar series of images by refracting the light that passes through them. In experiment 13, chapter 21 the method of studying the characteristics and position of the images formed is given. It will be found that as the object approaches the lens up to the focal plane the image formed on the opposite side of the lens is real, inverted, and gradually becomes larger in size as it moves farther from the lens. When the object is located inside the focal plane, the image becomes virtual, erect, and is located on the same side of the lens as the object. As in mirrors, so in lenses, it is possible to verify these results by means of simple geometric diagrams. To do so it is necessary to draw two rays from any point on object, and determine through what point they are focused by (Fig. 18:19). The two most the lens the suitable rays are; ( 1 ) A ray from the tip of the object parallel to the principal axis. This ray on passing through the lens is refracted principal through the focus., (2) A ray from the tip of the object through the optical centre of the Fig. 18:19 To Locate a Real Image in a Convex Lens. The point where these two refracted rays cross locates the tip of the image. A similar construction for other points on the object will locate the corresponding points on the image. Fig. 18:20 shows how to locate the virtual image obtained when the object is inside the focal plane of the lens. Fig. 18:20 To Locate a Virtual Image in a Convex Lens. The construction is identical to that just Because the refracted rays described. diverge from each other, it is necessary to produce them back to where they appear to meet. IV; 31 IMAGES IN CONCAVE LENSES By referring to experiment 14 chapter
21 it will be observed that concave lenses can form virtual images only. These are 207 Chap. 18 LIGHT always erect, smaller than the object, and located at less than the focal dis(Fig. 18:21). A tance from the lens close similarity will be noted between the images formed by concave lenses and those formed by convex mirrors (Sec. IV:16). Fig. 18:22 shows how the eye sees the Fig. 18:21 To Locate the Image of image produced by a lens. an Object in a Concave Lens. (b) Virtual Images. IV: 32 THE LENS FORMULAE The formulae we obtained for curved mirrors (Sec. IV: 18) also apply to lenses, that is, (a) Magnification Formula Height of Image Distance of Image FI eight of Object Distance of Object A fio~~ Do (b) Distance Formula Distance of Object Distance of Image Focal Length 1 + 1 = 1 D. D< f The same convention of signs must be followed, namely: real is posi- tive, virtual is negative. 208 REFRACTION OF LIGHT—LENSES Sec. IV:32 Examples 1. An object 5 cm. tall is placed 30 cm. from a convex lens whose focal length is 10 cm. (a) By means of an accurate scale diagram locate the image, and state its characteristics. Fig. 18:23 Scale 5 cm. = ^ in. (b) By using the lens formulae, determine the position of the image, and its size. How could you tell from your answer whether it is real or virtual? Do — 30 cm. Di —? 10 cm. / Do — + 1, 30 Di 1 / 1 Di~ 10 1 1 D~ 10 1 30 _ 3 — 1 ~ 30.'. Di=: 15 Note: Since the image distance i; + 15 cm., therefore the image is real..*. Imaae distance is 15 cm. Do = 30 cm. Di = 15 cm. Ho = 5 cm. H,=?..^_D, ’ Ho~ Do ‘. Hi _ 15 ~ 30 Hi = 2.5 5 Height of image is 2.5 cm. 209 Chap. 18 LIGHT 2. A concave lens has a focal length of 4 in. An object 1 in. high is 12 in. from the lens. (a) Determine the position and size of the image. (b) Verify
your answer by making an accurate scale diagram. / = — 4 in. Do = ( — since / is virtual) 12 in...Ill D~ f.•. 1 + '- = -1 12 Di 4. 1 _ 1 1 _ —3 —1.\Di = -3 Image distance is 3 in. Note: Since the image distance is negative, therefore, the image is virtual. Hi =? Ho = I in. Di = 3 in. Do= 12 in...Hi _1^ ‘ Ho~ Do ‘ ^- 1.''T~ 12.\Hi =. 25 Height of image is.25 in. IV: 33 APPLICATIONS OF LENSES part As lenses are an essential of almost every optical instrument, a discussion of their major applications is reserved until chapter 20 where several optical instruments are described. However, to relate specifically to the facts learned in the preceding sections we will mention a few simple uses here. The camera (Sec. IV; 44), (Sec. IV: 45), IV; 48) the telescope and the projection lantern (Sec. IV: 49) all contain a convex lens as an essential part of their construction. All these in- the eye (Sec. struments produce real, inverted images because the object viewed in each case is beyond the principal focus of the lens. (Sec. IV;46) In the magnifying glass and microscope (Sec. IV; 47) an enlarged, erect, virtual image is obtained because the object is inside the principal focus of the convex lens. Concave lenses are used along with convex lenses in many optical instruments to overcome certain defects, e.g., chromatic aberra(Sec. IV; 42), that would be apthe convex lens were used parent if tion alone. 210 REFRACTION OF LIGHT—LENSES Sec. IV: 34 IV : 34 QUESTIONS 1. 2. 3. A (a) Define refraction of light. (b) Describe and explain fraction of light as it passes obliquely from one medium into another of different optical density. the re- (a) Define index of refraction. (b) Draw a diagram showing how you can see a coin lying on the bottom of a dish filled with water, though the coin would be hidden if the dish contained no water. (c) What is the velocity of light in quartz? (See table p. 1 99 for index of refraction of quartz).
(d) The velocity of light in a diamond is 75,300 miles per second. What is its index of refraction? (a) How do you account for shimmering effect seen in the above a hot radiator? (b) How does the same principle account the twinkling the the for of air stars? 4. Place a thick glass plate on a line drawn on a piece of paper. View the line obliquely. Describe and explain what is observed. 5. aid of a diagram (a) With the explain why an oar appears bent when partly immersed in water and viewed obliquely. (b) Is the index of refraction greater for glass in which the velocity of light is 1 24,000 miles per second, or for water, in which the velocity is 1 40,000 miles per second? Why? 7. (a) Define critical angle. Illustrate your definition with a labelled diagram. (b) Would the be greater for water (Index of refrac- angle critical 8. 9. 1.33) or for glass (index of tion refraction 1.5)? Why? (a) Draw a diagram to show how a right-angled prism may be used to secure (i) one total internal reflection, (ii) two total internal reflections. (b) Explain why total reflection occurs in these two cases. (c) Why are total-reflection prisms preferable to mirrors in many optical instruments? (a) Compare the action of lenses to that of two prisms. (b) Define principal focus of a lens. (c) How can you determine experimentally the focal length of a lens? (d) Calculate the power of a lens whose focal length is 0.15 metres. 10. (a) What is the purpose of a sunlight recorder? (b) What approximate position relative to the glass sphere should the recording-belt occupy In the sunlight recorder? 11. (a) Distinguish between convex and concave lenses. (b) Summarize the types of images possible with both types of lenses and the conditions under which each is obtained. 12. An object is located at a point more than twice the focal length from a convex 6. (a) Define angle of deviation. lens. (b) State four factors that govern the amount of deviation produced by a prism. (c) Is the index of refraction of glass (a) By means of a diagram locate its image. (b
) State the characteristics of the image. constant for all colours of light? 13. (a) What do we mean by the magni- Explain your answer. fication produced by a lens? 211 Chap. 18 LIGHT 9. (b) How does the magnification depend on image distance and object distance? B 1. What is the index of refraction of a liquid in which the speed of light is 1 55,000 miles per second? 2. The index of refraction of diamond is 2.47; that of window glass is 1.51. How much faster does light travel in the glass than in diamond? 3. Light surface strikes the of glass making an angle of incidence of (a) 60°, (b) 45°, (c) 30°. The index of refraction of 1.5. By means of accurate geoglass is metric diagrams draw the refracted ray for each case. Using a protractor, measure the angles of refraction. 4. By means of an accurate construction determine the size of the angle of incidence when the angle of deviation is a minimum in an equilateral crown-glass prism. Measure the angle of deviation. 5. In which material does light travel faster, one with a critical angle of 25° or one with a critical angle of 30°? Explain, using appropriate diagrams. 6. An object 1 5 cm. high is located (i) 75 cm. (ii) 60 cm. (iii) 45 cm. (iv) 30 cm. (v) 20 cm. from a convex lens whose focal length is 30 cm. (a) By means of accurate scale diagrams locate of the image for each position of the object. (b) State the characteristics of each position the image. 7. By means of an accurate scale diagram locate the image produced by a concave lens whose focal length Is 1 5 in. of an object 6 in. high and 2 ft. distant. State the characteristics of the image. 8. A camera forms an image 8 cm. from the lens. If the object is 400 cm. away and 250 cm. tall, what is the height of the image? 212 The image of a tree in a miniature camera is 50 mm. from the lens and 30 mm. high. The tree is 1 5 metres away. How tall is the tree? 10. The image of an object 3 in. from a lens is formed 20 ft. from the lens. How many times is it magnified? 1 1. The
image of an object 24 ft. from a lens is focused clearly on a screen 3 ft. from the lens. What is the focal length of the lens? 12. A convex lens forms a virtual image at a point 1 2 cm. from the lens. The object distance is 8 cm. Find the focal length of the lens. 13. A tree 1 00 ft. from a camera lens has its image very close to the principal focus of the lens. If the tree is 66 ft. tall and the image is 4 in. tall, what is the focal length of the lens? 14. A candle is 1 2 cm. from a convex lens of focal length 8 cm. What is the distance from the lens to the image of the candle? 15. A student uses a convex lens to look at an object held 4 cm. from the lens. If the focal length of the lens is 5 cm., how far is the image from the lens? What kind of image is it? 16. The image in a camera is 1 0 cm. high and 1 4 cm. from the lens. If the object is 100 cm. tall, what is the focal length of the lens? 17. A jeweller uses a converging lens of in. to examine a diamond. focal length 1 The virtual image is 10 in. from the lens. Find (a) the object distance, (b) the magnifi- cation. 18. When photographing a scene at a distance of 6 ft. from the lens, you find that the distance between the lens and the film is 6 in. (a) What is the focal length of the lens? (b) What is the actual size of a portion of a scene which occupies a space 3 in. X 5 in. on the film? CHAPTER 19 COLOUR IV: 35 INTRODUCTION TO COLOUR Imagine how drab and uninteresting the world would be if there were no pleasure and colour. stimulation we receive from the colours of nature—the blue sky, the green grass, Think of the the beautiful flowers, the gorgeous hues of the sunrise and sunset. The use of colour in photography, in movies, and in book illustrations has added tremendously to our enjoyment of these things. How appealing and satisfying are some of the beautifully coloured mastei-pieces of art! Economically too, colour plays a very important role, as shown by the varied colours used in home decorating, clothing, advertising, and the like. For thousands of years
men have known that colourless glass of certain shapes, as well as frost, diamonds and other crystals, produce light of many colours when illuminated by white light. Sir Isaac Newton Until the time of everyone supposed that or crystals produced the light by giving something to the light as it was reflected by, or transmitted through, them. It was he who, after thorough scientific investigation arrived at the true explanation of the nature of colour and the character of white light. glass the IV: 36 COMPOSITION OF WHITE LIGHT (a) Dispersion In 1666, Newton permitted a beam of sunlight, passing through a circular hole in a window blind, to fall on a triangular glass prism. He found that the light was refracted or deviated, from its original Instead of obtaining a simple path. image of the hole, he obtained a band of colours which he called a spectrum. Its colours were the same as those found in the rainbow— red, orange, yellow, green, blue and violet, with each colour merging imperceptibly into the ne.xt (Fig. Red •Orange Yellow Green Blue Indigo Violet Fig. 19:1 Dispersion of White Light into its Spectrum. that Newton reasoned white 19:1). light must be composite, that is, made up of a combination of the above colours. The separation of the colours by the prism he called dispersion. A further study of dispersion is made in experiment 15, chapter 21. 213 Chap. 19 LIGHT.'As shown in Fig. 19:1 this dispersion occurs because the different colours are refracted different amounts by the prism and are deviated different amounts from their original direction. Red is always bent the least from its original direction and violet the most, with the other colours intermediate between these. Red light has the longest waves and violet the shortest, the wave-lengths of the other colours being between these two. the rays encounter less opposition to their passage through the glass prism and, therefore pass through more rapidly than do the violet rays. longer red Evidently, As we learned earlier (Sec. IV; 22), refraction is caused by a change in velocity of light on passing from one medium to another. In free space, or in air, light of all colours travels at the same rate, 186,000 miles per second. On entering an optically denser medium such as glass the light is slowed down, and on leaving this medium it speeds up to regain its original velocity in air. Since the different colours are bent different amounts by the prism
, it follows that they must be velocities through the prism. Red light, bent the least, must slow down the least on entering the prism and therefore speeds up the least on leaving. In contrast, violet light must slow down the most on entering, and speed up the most on leaving the prism. travelling different at A question that immediately arises of course is, “Why does the prism have this different effect on the different colours?” The answer relates back to our wave theory of light (Sec. IV: 7). The different colours of light result from different wave-lengths. Table of Wave-Lengths* (1 Angstrom (A) = 10'® cm. Infra-red above 7000 A Red Orange Yellow Green Blue ^ Visible Spectrum 6500A 6000A 5800A 5200A 4700A 4100A ^ Violet Ultra-violet below 4000 A [ * The wave-length shown for each colour is representative only. Each colour consists of wave-lengths that merge into those of the colours adjacent to it. For example, the wave-lengths of red lie between 6470 A and 7000 A. Colour bears the same relation to light that pitch does to sound. The pitch of a sound depends upon the number of vibrations per second that reach the ear Similarly the colour of (Sec. 11:12). light depends upon the number of vibrations per second that reach the eye. In light, however, since the frequency is so great, it is customary to describe the colour in terms of wave-lengths, rather than in terms of vibration frequency. Example Calculate the vibration frequency of red light. Velocity = 3X1 0^® cm. per sec ( Sec. IV : 6 ) Wave-length = 6500 A — 6500 X 10"® cm. Velocity = Frequency X Wave-length (Sec. 11:5) Frequency = Velocity Wave-length _ 3 X 1010 - 6500 X 10-8 =.46 X 1013 The vibration frequency of red light is.46 X lOi^ vibrations per second. 214 COLOUR Sec. IV: 36 Fig. 19:2 Recomposition of the Spectrum into White Light, (a) By Reversed Prisms, (b) By a Converging Lens, (c) By Newton's Disc. (b) Recomposition Newton further supported his theory concerning the composite nature of white light by showing that the colours of the spectrum could be recombined, giving white light (
Chap. 21, Exp. 16). He first arranged two prisms with their refracting edges in opposite directions. On passing white light through these reversed prisms, white light was obtained through Fig. 19:2a shows that the first them. prism disperses the colours, while the second prism recombines them by reversing the original refraction and causing the light waves to be superimposed on each other. A similar effect can be secured by using a converging lens to catch the dispersed coloured light from If this light is brought to a a prism. focus on a screen a spot of white light will be obtained (Fig. 19:2b). If the screen is moved beyond the focus, a rethe original colours will be versal of obtained. Newton also prepared a colour disc on which were coloured sectors whose sizes and colours corresponded fairly closely to the coloured bands obtained in a pure spectrum of white light (Fig. 19:2c). If this disc is strongly illuminated and rapidly rotated it will appear white. This phenomenon is due to what is called ‘the persistence of vision”. Any visual impression on the retina of the eye persists for a short period of time after the It is on this cause has been removed. principle that movies are made to appear continuous. In reality, each picture is thrown on the screen for a fraction of a second, its image persisting in our vision until the next appears. Similarly, if the coloured disc is rotated rapidly enough, the impression produced by one colour persists, while impressions produced by all the other colours are received on the same portion of the retina. Thus all the colours of the spectrum will be superimposed on the retina, and will give the sensation of white light. 215 Chap. 19 LIGHT IV : 37 THE RAINBOW The rainbow is a spectrum of sunlight formed by water droplets. A ray of sunlight entering a drop of water is refracted at A (Fig. 19:3a), the violet rays being refracted more than the red rays. Fig. 19:3 The Rainbow (a) Refraction and Total Reflection in a Raindrop. (b) The Primary Bow. (c) Double Reflection to Produce the Sec- ondary Bow. The refracted light is totally reflected at B and is again refracted at C so that the different colours are dispersed. Each drop of water forms its own little specIn the actual bow which the trum. observer sees, the red rays come at an angle of 42
° from drops of water higher 216 (Fig. in the sky, and the violet rays come at an angle of 40° from drops of water lower 19:3b). The other in the sky colours come from drops between these angles. The rainbow has the shape of a bow, since the eye of the observer is at the apex of a cone from which he sees the coloured rays refracted from drops, all of which must subtend approximately the same angle at the eye (between 40° and 42°). Sometimes a larger, but fainter secondary bow is seen above the primary. The colours in it are reversed, the violet being on the outside. The light enters the lower part of the water drops, is refracted, and twice totally reflected before it leaves the drop (Fig. 19:3c). The light is refracted from the drops of water at angles of from 51° to 54°. The double reflection not only reverses the colours, but also absorbs more light thus causing the secondary bow to be fainter than the primary bow. IV : 38 BEYOND THE VISIBLE SPECTRUM So far in our study of the spectrum we have considered only those radiations to which the eye is sensitive. Actually the spectrum of sunlight extends well beyond Sir William Herschel, its visible limits. in 1800, on placing the blackened bulb of a thermometer in the various parts of the spectrum, discovered that the heating effect observed at the red end was continued when the thermometer was placed well beyond the visible limit. He thus indicated the existence of a wide range of invisible radiation beyond the red end of the spectrum (Sec. 111:15). These infra-red radiations, as they are called, convey almost half of the sun’s total outpouring of energy into space. They can penetrate mist, smoke and haze and hence are very suitable for distance photophotography, graphy in the dark, and detection of reconnaissance, ^ <c ^ III 3 \| i 0) -c ^ ^ I <D "D Q- c s D I c c O (D o O) S •4^ Q. O O "D ^ ^-2 < fi-g O O O _C CO — CO u -tu C <13 1 °? CO Q. to LU O Frequency 10 H lo' lO' 10- lo"- 10 lO'-l 10 lo'H - 12 10 10 - 10 10 * — lo' lo' lo' lo
active substances). radiations are propagated as waves with the same velocity as light, the difference in their properties being due to their different wave-lengths. The relationship between these various electromagnetic is shown waves, diagrammatically in Fig. 19:4. as they are called, IV: 39 SPECTRUM ANALYSIS The spectroscope is an important instrument by means of which the spectra of luminous bodies can be produced and measured. It consists of a tube called the collimator (Fig. 19:5), at one end of which is a convex lens and at the other end an adjustable vertical slit. The length of the tube is equal to the focal length of the collimator lens, so that when the slit is illuminated by light from the source, S, under examination, a parallel beam can be directed onto a prism situated on a small turn-table at the centre of the instrument. The dispersed beams produced by the prism are received by a telescope focused for parlight and fitted with cross-wires. allel This telescope can be moved round a circular scale against which the deviations of the constituent parts of the spectrum formed can be measured. The this way of the light examination in from different luminous bodies reveals that each spectrum is characteristic of the source, and a study of these spectra yields much valuable information to the physicist and astronomer. Accordingly we shall briefly consider here some of the more important spectra and their significance (Fig. 19:6), Continuous Spectra: These consist of a number of coloured bands each shading off gradually into the next. They are produced by incandescent solids, e.g., arc-lamps, white-hot iron, etc. Incandescent gases and Line Spectra: vapours emit light which when analysed produces spectra consisting of a number of well - defined coloured lines or col oured images of the slit. Each element has its own characteristic line spectrum which provides a certain and accurate means of identifying the element (Exp. 17, Chap. 21). The presence of even a minute quantity of an element in a mixture can be detected by spectroscopic analysis, and it is interesting to note that the method has been the means of discovering new elements. If the spectrum of a substance contains lines which do not correspond with those of any known element, the obvious conclusion is that there is present an element as yet not known. In this way the elements caesium and rubidium were discovered by Bunsen. Line spectra can be produced by
the Bunsen flame only in the case of subvaporized. stances Other substances must be vaporized, using an electric arc or a spark dis- which easily are Fig. 19:7 An Electrical Discharge Tube. The spectra of incandescent charge. gases are usually obtained by means of special tubes containing a sample of the gas at low pressure through which the discharge from an induction passed (Fig. 19:7). coil is Absorption Spectra: If a sodium flame is set up between the slit of a spectroscope and a high-power electric lamp (Fig. 19:8), a dark line will be observed in the continuous spectrum of the light from the relatively hotter lamp in a position corresponding to that of the 219 Chap. 19 LIGHT yellow line of the incandescent sodium vapour. With other vapours dark lines would be formed in positions corresponding to their line spectra. A spectrum Fig. 19:8 The Production of an Ab- sorption Spectrum. crossed by dark lines in this way is called an absorption spectrum, and it was found that all substances when interposed in the path of light originating from a higher temperature source absorb from it light of the same wave-length that they themselves emit. Most of the The Solar Spectrum is an absorption spectrum containing hundreds of dark lines carefully studied by Fraunhofer in 1814. These lines are due to selective absorption from the radiation emanating from the extremely hot core of the sun by the relatively cooler gases in the sun’s atmosphere. lines have been found to correspond to lines in the spectra of elements present on the earth, and we have thus good grounds for believing that the chemical components of the sun and the earth are similar. A certain group of lines did not correspond with those of any known element. They were accordingly attributed to an element which was named helium, and which was ultimately discovered on the earth twenty-six years later. The constitution of the stars is determined in a similar way from an examination of their absorption lines. IV : 40 NATURE OF COLOUR (a) Colour We have that colour is a property of light waves (Sec. established already 220 It may be defined generally, IV; 36). as the response of vision to different wave-lengths of light. Colour is the alphabet in our visual language, through which we make interesting our description of things and ideas which otherwise would be dull and prosaic. Our present knowledge and use of colour is based largely on the sciences of psychology, chemistry, and physics
. Psychology considers colour through the physical operation of the eye and the mental impression created by colour on the brain. As a result, the actual perception of colour is a highly personal experience which may be influenced by such factors as health, fatigue and response of the eye to colour (colourAccording to psychologists blindness). the average person recognizes four distinct primary colours, red, yellow, blue and green. Colours do have a strong influence on people. Tensions can be heightened or relaxed through a change in colour harmonies; a feeling of warmth or coldness can be obtained by colour schemes used; colour can be stimulating or restful, it can attract or it can repel. Chemistry deals with the production of materials which have the ability to absorb or reflect part of the light which falls upon them. These are chiefly dyes and pigments. The explanation for the colours of these materials is given in part (b) below. Physics deals with colour from the standpoint of differences in wave-lengths of the coloured lights, and the effects of superimposing these on one another. The additive theory of colour to explain (c) these effects is discussed in part below. These three colour theories are the basis for our modern usage of colour. Though separate, they are also interdependent. The range and intensity of the colours we see depend upon the quality and quantity of light, the nature of the. COLOUR Sec. IV: 40 surface visible, and our ability and interpret what meets our eyes. to see (b) Colour of Objects— The Subtractive Theory There are three colours, yellow, red, and blue, which in pigments are the source of all other colours. By mixing these three colours in the right proportion, all other colours may be obtained. No mixture of other colours will produce any of these three colours. For this reason yellow, red, and blue are called primary colours. A colour chart has been prepared (Fig. 19:9) in which these primary colours are placed the same distance apart along the edge of the circle. Mixing any two primary colours produces a third colour called a binary colour which is intermediate between those primaries, e.g., yellow and red produce orange. Various hues can be produced by mixing a binary colour with a primary colour used in making the binary, e.g., yellow and orange produce yellow orange. Certain colours seem to strengthen each other when they are seen together, and hence are said to be complementary to each other. In the chart the colours on the opposite sides of the
circle are complementary. White is the total addition of colour, is of then, the result spectrum, and reflects and not, as often believed, the absence of colour. It is produced when a surface reflects all colours equally. Black, on the other hand, is perceived when a surface absorbs all colours and reflects none. Colour, partial absorption, and consequent subtraction, of a band of colour from the spectrum. The surface of an object will appear red when it is of such nature that it absorbs all but the red wave-lengths of red the wave-lengths (Chap. 21, Exp. 18). When we mix pigments, each one subtracts certain colours from white light, and the resulting colour depends upon the light that is not absorbed. For example, if we mix a blue pigment with a yellow one we get a green colour. The blue colours from subtracts or absorbs all white light, except green, blue and violet, while the yellow subtracts all except green, yellow and orange. Green is the only colour not subtracted by either pigment. For this reason the two pigments produce green. these Similarly, transparent objects are able certain colours to absorb or subtract from white light. If white light is passed through a piece of red glass, the glass absorbs all light except red, and a little orange, and we obtain red light (Fig. 19:10a). Objects that are transparent to only one colour are called colour filters. The combination of a yellow and a blue filter placed over a single white light source will result in a green light because all except the green wave-lengths of the spectrum have been absorbed a combination of three filters, each corresponding to a primary colour, will absorb all the colours and allow practically no light to pass (Fig. 19:10c). (Chap. 21, Exp. 18) 19:10b). Similarly (Fig. The light which falls upon an object can also determine its colour. If the light does not contain all the colours of 221 Chap. 19 LIGHT RED YELLOW BLUE (a) (b) Fig. 19:10 Colour Filters (The Subtractive Theory) (a) Transmission of Light by Different Coloured Filters. (b) Combination of Yellow and Blue. (c) Combination of Red, Yellow, and Blue. o the spectrum then the true colour of the object will not be observed. The light given off by a light bulb does not contain all the colours found in sunlight. For
this reason an article of clothing may appear quite different in the sunlight than when seen under artificial light. (c) Coloured Lights— The Additive Theory Having produced different coloured lights by the use of filters, two or more of these may be added together to produce still other colours. The three colours, red, green and blue, which combine to produce white are called the three primary colours for lights. None of these primary colours can be produced by adding other colours of lights. However, any other colour can be pro- 222 19:11). duced by a proper combination of them For example, red and (Fig. blue light when combined produce violet; red and green light added together Fig. 19:11 Coloured Lights (The Ad- ditive Theory). COLOUR Sec. IV: 41 will produce yellow, and so on. The colour resulting from the simple combination of each pair of primary colours is complementary to the third primary; for example, violet is complementary to green, and yellow is complementary to If we superimpose these comblue. plementary coloured lights we again get white light. Contrast how colour is obtained in mixing pigments with how it is obtained in mixing coloured lights. In the former the resulting colour is the one not absorbed or subtracted by either pigment in the latter the (the subtractive effect) ; resulting colour is obtained by adding the effect of the individual colours (the additive effect). Both methods are widely used in industry. The mixing of pigments to produce our multi-coloured paints, the many vegetable and synthetic dyes for treating fabrics, etc., and the use of filters in photography, all are applications of the subtractive effect mentioned above. The additive effect is applied in the use of coloured spotlights to illuminate actors on stage, or participants in a carnival or pageant, as well as to produce changing and spectacular effects in the illumination of Niagara Falls and in some of the coloured advertising that is so common nowadays. textiles, Colour is of tremendous importance Its use in advertising has in industry. been mentioned above. Bright contrasting colours of paint on walls, floors, and machinery not only provide better visual conditions but also boost morale, speed up production, and affect safety re- cords. Colour codes are used in busi- ness for invoicing, in electrical indus- tries to denote polarity, voltage, resistance, and the like, and in shipping to encourage due precautions in the han- dling of dangerous articles. All, of course, are familiar
with its use in traffic control. (d) Colour Vision are there theory, widely The way in which light is changed into the sensation of sight is not definitely The most known. accepted the Young-Helmholtz theory, of colour three states nerves in the normal eye. One of these sets of nerves responds only to blue light, another set to green light, and the third set to red light. The colour of an object is determined by the relative degree of stimulation of each type of nerve. sets A small proportion of men (about 3/2%) and women (about ^2%), do not have all three of these sets of colour nerves and hence they do not receive the same sensation of colour from an object as a person with all three sets of colour nerves. Such people are said to be colour blind. By this we do not mean that they do not see colour in objects, but that they do not see the same colours as a person with normal eyes. This defect through inherited is usually exists from birth; and there is no known cure for it. it mother; the pattern Because a colour-blind person sees a different colour pattern in a landscape seen by a person from the having normal vision, colour-blind observers are very efficient in detecting camouflage and are so used during wars. Some colour-blind persons are unable to distinguish reds and greens from each other and, consequently, have real difficulty with traffic signals. IV: 41 COLOUR PRINTING Most of the coloured pictures in books and magazines are made by using four separate printing-plates, each plate printing a different coloured ink on white paper—yellow, red, blue and black, in that order. The plates are made from four photographic negatives of the same are made negatives subject. through These fine-meshed coloured filters. 223 Chap. 19 LIGHT the the creation of each stained with one of three primary colours (the black one is not the actually used in Fig. 19:12). The coloured picture in fine-meshed filter breaks the subject into numerous small dots on the negative. The filter determines what colours can pass through the camera and become recorded on the negative. Thus dots representing only certain colours are recorded on each negative. The first plate reproduces the dots of the first negative in yellow ink on white paper. The second plate reproduces those of the second negative in red ink on or between the yellow dots, etc. The final effect is one of individual and overlapping dots of colour. Where a dot of one colour overlaps a dot
: spectrum, dispersion. (b) Why does a prism deviate violet light more than red light? (c) Calculate the vibration frequency of violet light (See table, p. 214, for wave-length of violet light). 2. Describe and explain three methods for recombining the spectral colours into white light. 3. Explain how refraction produces a solar spectrum (rainbow). 4. Write a note on (a) infra-red rays, (b) ultra-violet rays, indicating, (i) how each differs from visible light. (ii) how each can be detected. (iii) how each is used. (a) What is the purpose of a spectroscope? 5. 8. (i) a continuous (b) Distinguish a line spectrum from an absorption spectrum. How is each produced? spectrum, (ii) (c) Why does red glass appear red, blue glass appear blue, and ordinary glass appear colourless, white light? State a general rule for the in colour of transparent objects. (d) What would be the colour of the objects in (b) when viewed through (i) a red-glass filter, (ii) a blue-glass filter? (e) Why is it unwise to buy coloured clothing by artificial light? (a) How does the additive theory of subtractive light differ from the theory? (b) In the additive theory what are (i) the primary colours, (ii) complementary colours? (c) If coloured spotlights are shone on a white screen, (i) what colour will be obtained if red and blue lights are used? (ii) what coloured used to produce yellow? lights should be 6. What is the physicist’s explanation of (a) coloured light, (b) white light? 7. (a) In the subtractive theory of light what are (i) the primary colours, (ii) complementary colours? (b) Why does a rose appear red, grass green and a dandelion yellow when seen in sunlight? State a general rule for the colour of an opaque object. 9. How does the physicist account for the difference between mixing coloured lights and coloured pigments? 10. What is colour-blindness? How does the Helmholtz theory explain it? 11. Describe the process of colour print- ing. 12. (a) What is chromatic aberration? (b) What is an achromatic lens? 225 CH
APTER 20 OPTICAL INSTRUMENTS 1553, Porta, Baptista and camera. Johann Kepler, 1604, later added a lens and then a combination of lenses. From these simple beginnings have come many types of cameras ranging from the relatively inexpensive family-type cameras, through the more expensive press and movie cameras, up into the highly specialized cameras used in television and in aerial photography. (b) Structure All cameras are constructed on the same basic principles as were the first crude, wooden, box-cameras. The essential parts of a camera (Fig. 20:1) are: 1. A light-tight box or bellows. 2. A lens to form the image on the film. 3. A shutter (and diaphragm) to con- IV : 44 THE CAMERA The photographic camera is essentially an enclosed box or bellows chamber with an opening or aperture in the front through which light from an object The image is recorded on a passes. light-sensitive material at the back. (a) History The evolution of the camera is credited to men like Roger Bacon, 1267, and Leonardo da Vinci, 1519, who dedeveloped pin-hole scribed and the 226 OPTICAL INSTRUMENTS Sec. IV; 45 the amount of trol admitted to the film. light that is 4. A negative holder or carrier to hold films in position during exposure. 5. A view-finder or ground glass to determine picture area. By the addition of special accessories and other refinements, the utility and scope of the camera may be extended to meet almost any photographic requirement. (c) Focusing In order to focus objects at different distances from the camera, the lens is often attached to a bellows so that it may be moved nearer to the light-sensitive plate or film, or farther away. In section IV : 30 we learned that as the object is moved nearer to a converging lens, the real inverted image gradually moves farther away from the lens. This should indicate how to focus the camera. For distant objects the lens is moved so that the sensitive plate is located at its principal focus. For close objects, the lens is moved away from the sensitive film, for now the image is focused beyond the principal focus of the lens. Most cameras include a focusing scale on the lens mount or on the bed of the camera and many have built-in range finders to assist in focusing. (d) Light Control As has been indicated previously the film or plate in a camera
contains materials which are sensitive to light. The plate is coated with an emulsion consisting of gelatine and a silver salt. Light decomposes this silver salt so that when “developed” and “fixed” a negative is obtained consisting of a dark deposit of silver in places corresponding to the light parts of the original image, and light transparent portions in positions corresponding to the darker parts of the original image. One sees, therefore, that it is necessary to be able to control the amount of light that enters the camera. This is done in two ways : ( 1 ) by controlling the size of the aperture or opening through which the light enters; and (2) by regulating the length of time that the light is permitted to enter. The former is accomplished by using a variable diaphragm behind the lens which enables the aperture to be varied, and the latter by means of a shutter, which is a delicate mechanical device, often consisting of a number of overlapping thin metal blades, held in position by means of springs. On being released or tripped, when taking a picture, the shutter opens and closes for a measured time interval. When using a small aperture a longer exposure is required than with a large It is wise practice to use as small one. an aperture as possible as this permits using the central part of the lens only, and prevents errors due to inaccuracies near the edges of the lens. Also greater depth of focus is obtained, that is, objects relatively smaller and greater disstill be at tances from the camera will sufficiently in focus to look clear in the print. IV: 45 THE HUMAN EYE to be perceived. The eye is the sense organ enabling This, the most light wonderful of all optical instruments, can be compared in many respects to a camera (Fig. 20:2). (a) Structure and Action The eyeball is approximately spherical in shape and slightly less than one inch in diameter (Fig. 20:3). The wall of this sphere is composed of two major layers: ( 1 ) the outer covering, the sclerotic coat, substance forming the white of the eye. The front portion of this sclerotic coat forms a transparent, curved section called the tough opaque white a is 227 Chap. 20 LIGHT Fig. 20:2 Comparison of the Eye and the Camera. cornea that protects the eye and aids in refracting light. (2) The inner layer, the choroid coat, is black to prevent internal reflection and to protect the light-sensitive
parts of the eye. is also largely nutritive in function. The aqueous and vitreous humours are jellylike materials filling the spaces within It the eyeball, which help to keep its spherical shape. Behind the cornea is a coloured diaphragm called the iris. This is really an Fig. 20:3 The Structure of the Eye. 228 extension of the choroid coat, and its colour is mainly due to the variable amounts of pigment in it. In the centre of the iris is a circular aperture, called the pupil, which appears black due to the black interior of the eye. The iris contains muscles, which dilate and contract the pupil adjusting the eye to different amounts of light. The pupil is dilated in dim light, and contracted in bright light. This action occurs involuntarily, i.e., without any control on our part, and hence is called the iris reflex. To note its action, stand in front of a mirror in a dark room for several minutes. Then turn on the light and note the immediate contraction of the pupil. Optometrists use drugs, such as atropine, to temporarily dilate the pupil and permit internal examination of the eye. Behind the pupil and iris is the crystalline lens. This is a transparent structure, made up of numerous concentric layers, increasing in density toward the middle. OPTICAL INSTRUMENTS Sec. IV: 45 it so that tension The curvature of its front surface is considerably less than that of the back Both of these features tend surface. to diminish distortion of the image. The lens is encased in an elastic capsule and is held in place by suspensory ligaments which are attached to the choroid coat. These ligaments hold the lens under a normally certain tends to be flattened and adjusted for distant vision. In the choroid layer near the suspensory ligaments are small ciliary muscles. The contraction of these muscles tension exerted by the suspensory ligaments on the lens which therefore becomes more convex and so adjusted for close vision. The adjustment of the lens to form a sharp image on the retina is called accommodation (Fig. 20:4). The normal eye can accommodate itself to objects ranging from infinity to a point about twenty-five ten inches from the eye. This latter point is known as the nearest point of distinct Objects closer to the eye than centimeters or relieve vision. tends the to • Distant Vision (b) Close Vision. this cannot be clearly
focused by the unaided eye. their characteristic The retina is the innermost layer of the eye and is sensitive to light. The retina is composed of visual cells, nerve cells, and the fibres which connect these and conduct the nerve impulses to the brain. The visual cells are of two types, called rods and cones, so named because rod and cone of shapes. The rods are concerned with colourless and dim-light vision, while the cones handle colour and bright-light vision. The nerve cells integrate and relay the impulses which they receive, to the optic nerve, and through it to That part of the retina where the optic nerve enters the eye, is insensitive to light and is known as the Its existence can be readily blind spot. demonstrated as shown in Fig. 20:5. The most sensitive part of the retina is a small yellow spot located on the principal axis of the lens. An object being viewed is automatically focused on this brain. the area. X Fig. 20:5 The Blind Spot. Close one eye. Hold the book at arm's length. Stare at the X. Move the book toward you. At a certain distance the circle will disappear, for its image is formed on the blind spot. 229. Chap. 20 LIGHT (b) Defects of Vision and Their Correction In view of the delicate adjustments made by our eyes and the way we abuse them these days with excessive reading, watching movies, television, only natural that many abnormalities or defects develop. Here, however, we are only concerned with defects or errors caused by refraction of light. etc., it is is rest, parallel When an eye with no refractive error rays of light are at focused exactly on the retina. Many eyes, owing to abnormalities of the refracting mechanism, do not focus the light exactly on the retina. Such defects of the eye can in large measure be overcome with the (spectacles) of suitable lenses aid /. Near-sightedness to close Persons suffering from this defect are unable to focus on distant objects distinctly, although objects the eyes are clearly seen. This is due to the axis of the eyeball being too long or the crystalline lens being too powerful, so that rays from a distant object tend to be focused in front of the retina (Fig. This defect is largely heredi20:6a). also aggravated by too strenuous use of the eyes during the early years. Concave lenses placed in front of the eye will make the light more divergent and bring the image to
a focus on the retina. but is tary, 2. Far-sightedness A far-sighted person cannot see clearly objects close to the eye although distant objects may be distinctly The defect is due to the axis of the eyeball being too short or the crystalline lens not sufficiently converging so that rays from a nearby object tend to converge seen. to a point behind the (Fig. It is the most common of re20:6b). fractive errors of the eyes and is present retina 230 to some degree in about two-thirds of all adults. Convex lenses placed in front of the eye will reduce the divergence of the rays which can then be focused on the retina. (c) Fig. 20:6 Defects of Vision. (a) Near-sightedness, Corrected by Con- cave Lens. (b) Far-sightedness, Corrected by Con- vex Lens. (c) Test for Astigmatism. the lines appear equally distinct to you? Do all 3. Astigmatism As a result in different planes are brought to different foci and in consequence one set of lines of this defect lines OPTICAL INSTRUMENTS Sec. IV: 46 (Fig. 20:6c). will be in sharp focus, while others inclined to them are blurred and indisFor example, an tinct astigmatic eye may clearly discern all the vertical lines of a building, while those in a horizontal plane are scarcely perceived. The main cause of this defect is the lack of sphericity of the cornea, in which the vertical section is frequently more curved than the horizontal. To overcome the defect cylindrical lenses are used to assist refraction in the plane of least curvature of the cornea. Astigmatism is present to varying degrees in most eyes. ing rays from the object without undue With the use of a short-focus strain. convex lens, however, it is possible to bring the object even closer, thereby enabling it to be seen still more distinctly without straining the eye. The object is placed inside the focus of the lens at such a position that the eye focuses the magnified virtual image formed at the nearest point of distinct vision. The path of the rays by which the eye sees the image is shown in Fig. 20:7. The magnifying power of such a lens the size of image on retina when is object is viewed through the lens divided 4. Presbyopia It loss This is a defect of age resulting from of accommodation brought the about by
hardening of the crystalline lens, or of the ciliary muscles. is evidenced by both near and far objects being indistinct. Clear vision by the unaided eye is possible over only a very restricted range. Two pairs of spectacles are required by such people, one pair (convex) for reading, and another pair (concave) for distant vision. Both purposes may be served by a pair of bifocal lenses, the top part being used for distance, and the lower part for reading. IV : 46 THE MAGNIFYING GLASS The apparent size of an object depends on the angle it subtends at the eye. This angle is known as the visual angle of the object, and in order to see a small object clearly one instinctively brings it close to the eye, with consequent increase in its visual angle. With the unaided eye there is, however, a limit to which this process can be carried. This is reached when the object is at the nearest point of distinct vision (normally 25 cm. or 10 in.) at which position the object is seen most clearly. If brought within this natural limit the eye cannot accommodate itself to the widely diverg- The Action of a MagnifyFig. 20:7 ing Glass. The image is focused at the least distance of distinct vision. by size of image on retina when object is viewed directly at the least distance of distinct vision least distance of distinct vision focal length of the lens 10 in. 25 cm. In using a magnifying glass we focus the image at the least distance of distinct vision by moving the lens back and forth from the object. A near-sighted person might focus on an image 7 inches from the eye, for example, whereas a far-sighted person would change the lensobject distance so that the image might be 13 inches from the eye. If / 1 inch., the former person would only get a magnification of 7 X, whereas the farsighted person would get a magnification of 13 X. To save argument the average value for least distance of distinct vision has been set at 10 inches. 231 a as simple magnifying principal focus, F', of the eyepiece which acts glass. Through this lens the eye sees a large virtual image, pq, when the length of the tube is properly adjusted so that the image is sharply in focus at the nearest As with the point of magnifying glass, position of the the virtual image depends upon the accommodation of the observer’s eye. distinct
ESCOPE (a) Refracting Telescope The method by which the telescope works is similar to that of the microscope. The refracting telescope consists be the focal larger length of an arrangement of two convex lenses for viewing very distant objects (Chap. 21, Exp. 19), The objective should have a very great focal length, for the greater the will the image of an object at infinity. It should also be of large diameter to enable a maximum amount of light to be collected, thereby producing a brighter image. This lens will produce a real inverted image at its principal focus. This should be located just within the principal focus of the eyepiece through which the eye sees a magnified virtual image (Fig. 20:9). The magnifying power of the telescope is approximately equal to the focal length, F, of the objective divided by the focal length, /, of the eyepiece. Magnifying power = — Fig. 20:10 Two Forms of the Reflecting Telescope. 233 Chap. 20 LIGHT Palomar Mountain Observatory, California. Star Newspaper Service (h) Reflecting Telescope Reflecting telescopes are used for astronomical purposes. The objective is a parabolic mirror (Sec. IV; 19) which light from the distant object. collects Since the light is reflected back toward the object, a means of viewing the image with an eyepiece necessitates the use of an additional mirror or prism 20 : 10 ). (Fig. Large reflecting telescopes include the 74 inch diameter telescope at the David Dunlap Observatory at Richmond Hill, Ontario, and the 72 inch telescope at the Dominion Observatory near Victoria, British Columbia. Larger Astro-Physical telescopes of this type are located at Mount Wilson, California (100 in.) and at Palomar Mountain, California (200 in. ). This latter is the largest telescope in the world, having one million times the light-gathering power of the human eye. (c) Terrestrial Telescope The drawback to the astronomical telescope is that the image is inverted. For observing familiar terrestrial objects a telescope requires an image-erecting system. The simplest means of obtaining this is to insert a third convex lens to re-invert the image (Fig. 20:11). Such terrestrial telescopes are used by surveyors, by mariners and by military men. Final Image First Image 234 OPTICAL INSTRUMENTS Sec. IV; 50 Fig. 20:12 The Slide Projector. IV: 49 THE SLIDE PROJECTOR The purpose of the slide projector is
to cast a magnified image of a slide or transparency upon a screen coloured some distance away. Fig. 20:12 shows the essential structure of such a projector. A study of the paths of the light rays shown in the diagram will serve as an excellent review of some of the work covered earlier in concave mirrors and converging lenses. For this instrument a very powerful light source is needed. This is placed at the centre of curvature of a concave reflector (mirror) M, so that many rays that tend to be lost, on hitting this mirror are reflected back on themselves thereby intensifying the light source. It is also placed at the principal focus of is this condenser a condensing lens system, C. As a result the diverging cone of rays from the light source on striking concentrated into a parallel beam of light and sent through the slide, O. The slide must be located outside the principal focus of the objective, L. This lens as a result produces a real, enlarged, and inverted image on the screen. The slide is always inserted upside down in the carrier, so that its image will be erect on the screen, /. The size of the image may be increased by increasing the distance between the projector and the screen. The objective is contained in a moveable mount, to permit focusing the image for different distances of projecOptically the motion-picture pro- tion. jector and slide projector are similar. 3. IV: 50 QUESTIONS 1. Compare lens camera and the human eye under the following headings: contrast the and (a) structure. (b) focusing. (c) light control. (a) an object close to the camera. (b) an object distant from the camera. (c) an object on a cloudy day. (d) an object on a sunny day. (e) a moving object. The focal length of a camera lens is 2. What adjustments would you make in your camera for taking pictures under the following conditions: 3.0 in. (a) How far from the film is the lens when a man standing 1 2 ft. from the 235 (a) Make a sketch of a compound microscope locating the two images, (b) If the first (objective) lens magnifies the object 8 times and the eyepiece magnifies the real image 20 times, how many times is the final image larger than the object? 8. Discuss (a) the refracting telescope, (b) the reflecting telescope and (
c) the terrestrial telescope, as to: 9. (i) essential parts. (ii) how each works. (iii) types of images obtained. In a slide projector: (a) Where is the light source relative to (i) the concave reflector, (ii) the condensing lens? Why is it placed in this position? (b) Where is the slide relative to the principal focus of the objective lens? In what relative position is the slide inserted in the carrier? Why? (c) If the image formed by the projector is too large for the screen should you move the projector closer to the screen or farther away from it? Why? What further adjustment would be necessary? (d) The object is 16 mm. high and 50 mm. from the lens. If the screen is 6 metres away, what b the height of the image? Chap. 20 LIGHT camera is brought into focus upon the 7. film? (b) How tall will be the man’s image on the unenlarged picture his if 4. iris reflex, height is 6 ft.? (a) What is meant by (i) (ii) lens accommodation? (b) Why do your eyes become more sensitive when you go into a darkened room? (c) By means of a diagram show how the lens of the eye changes when the object viewed is moved closer to the eye. 5. Describe, with the aid of diagrams, (a) near-sightedness, (b) far-sightedness, (c) astigmatism, under the following head- ings: (i) cause. (ii) effect. (iii) correction. 6. (a) What is the purpose of the magnifying glass? (b) Describe the image you see through a magnifying glass. (c) Calculate the magnifying power of such a glass having a focal length 1,5 in. of (i) 3.0 cm, (ii) (d) What would be the size of the image of a crystal 3 mm. long when viewed through each of the magnify- ing glasses in 6 (c)? 236 CHAPTER 21 EXPERIMENTS ON LIGHT EXPERIMENT 1 To study the characteristics of an image produced by a pin-hole camera. (Ref. Sec. IV: 4) Apparatus Pin-hole camera (Fig. 16:3), one large candle, one small candle. Method 1. With the adjustable section
of the camera held stationary so that the ground-glass screen is a fixed distance from the pin-hole, observe the size and other characteristics of the image of the candle placed at some distance from the camera. Move the camera closer to the candle and note the size of the image. 2. Holding the camera a fixed distance from the candle, note the size of the image. Move the adjustable section thereby decreasing the distance of the screen, and hence of the image, from the pin-hole, and again note the size of the image. 3. With the adjustable section held stationary as in step 1, observe the size of the image produced by first the large, and then the small candle at a fixed distance from the camera. 4. If possible, enlarge the pin-hole and note the effect on the brightness and sharpness of the image. Observations Record carefully the observations for each of the previous steps. Conclusions 1. State the characteristics of the image. 2. What effect did each of the following have on the size of the image: (a) decreasing object distance? (b) decreasing image distance? (c) decreasing size of object? 3. Establish the formula: Hi Di Ho~~Do 4. On what does the brightness of the image and its sharpness of defini- tion depend? Explain fully. 237 Chap. 21 LIGHT Questions 1. Why do we get an image of the candle and not an image of the pin-hole? 2. What image would be obtained if the hole were increased in size until it has a diameter of 1 in. or more? Why? EXPERIMENT 2 To establish the laws of reflection. (Ref. Sec. IV: 9) Apparatus Plane mirror, pins, sheet of paper, tack board, ruler, protractor. Method A. Demonstration Experiment—Optical Disc Method (Sec. IV: 9). B. Student Experiment^—-Pin Method. 1. Draw a straight line AB (Fig. 21:1). Place the mirror perpen- dicular to the paper so that its back edge is along this line. 2. Place pins at P and Q about 2 in. apart so that the line PQ strikes the mirror obliquely. 3. Look into the mirror with one eye at the level of the paper and line up the images of P and Q. Insert pins R and S in line with these images. 4. Mark the position of all the pins. Remove the mirror and the pins. Draw the lines
PQ and RS. Produce these lines until they meet at T. Through T draw TN perpendicular to AB. With a protractor measure angles PTN and STN. 5. Repeat, with other positions of the pins. Observations 1. Observation No. Angle of Incidence Z PTN Angle of Reflection Z STN 1. 2. 3. 238 EXPERIMENTS ON LIGHT 2. When the incident ray is on the plane of the paper where are the reflected ray and the normal found? Conclusions 1. State the two Laws of Reflection. 2. Define, and label on your diagram: incident ray, reflected ray, point of incidence, normal, angle of incidence, angle of reflection. Questions 1. If a polished piece of metal were used as the mirror in the above experiment, where would T be found? Why? 2. Add an observer’s eye to the diagram and trace the path of the rays to the eye. EXPERIMENT 3 To study the position and characteristics of the image in a plane mirror, (Ref. Sec. IV: 11) Apparatus Plane mirror, two wooden pegs, paper, ruler, protractor. A Mb — izi-:. I o Fig. 21:2 Method 1. Draw a straight line AB in the middle of the sheet of paper. Place a plane mirror perpendicular to the paper, so that its reflecting surface is on AB. 2. Place the object (wooden peg) about 3 in. in front of the mirror. Mark its position O. 3. Look into the mirror to see the image of this object, and using the second wooden peg as a finder place it exactly where the image This can be done quite accurately by using the appears to be. method of parallax. That is, look into the mirror at the image, and over the top of the mirror at the finder. Adjust the position of the latter so that when you move your eye from side to side there is no relative movement between the finder and the image. Mark the position of the image I. Compare the size of the image to the size of the object. 239 Chap. 21 LIGHT 4. Remove the mirror. Join OI and let the line cut AB at M. Measure the lengths of OM and IM, and measure the sizes of the angles at M. 5. Repeat for other positions of the object. 6. Look at yourself in a mirror and raise your left hand. Note
what you see. Observations 1. Observation Number Distance of Object OM Distance of Image IM Size of Angles AT M 1. 2. 3. 2. How does the size of an object and its image compare? 3. Which hand appeared to be raised in the mirror? What term applied to the image describes this phenomenon? 4. What kind of image is it? Conclusions 1. State your conclusion relating to the position of an image in a plane mirror. 2. Summarize the characteristics of such an image. 3. Define or explain; parallax, lateral inversion, virtual image. Questions 1. How could you locate geometrically the position of the image of an object in a plane mirror? Show this by a diagram. 2. Include in the diagram an eye, and show the path of the light rays whereby the eye sees the image. EXPERIMENT 4 To show the location of images produced by two plane mirrors at right angles. (Ref. Sec. IV: 13) Apparatus Two plane mirrors, four wooden pegs, paper, ruler, protractor. Method Repeat parts 1, 2 and 3 of experiment 3 using two plane mirrors placed at right angles to each other. Observations Describe the number and location of the images. Conclusion Construct a diagram to show how the images were obtained. 240 EXPERIMENTS ON LIGHT Questions 1. Add an observer’s eye to the above diagram and trace the path of the rays to the eye. 2. Determine experimentally how many images are obtained when the mirrors are inclined at 60°, at 45°, etc. Use your results to verify the formula; Number of images = 360° —— : ; angle ol inclination 1 EXPERIMENT 5 To study the action of a concave mirror, and to determine its focal length (f), (Ref. Sec. IV: 14) Apparatus Optical bench, concave mirror, candle, screen. V D 1'U. Fig. 21:3 J U Method A. Demonstration Experiment—Optical-Disc Method (Sec. IV: 14). B. Student Experiment—Optical-Bench Method. 1. Mount the concave mirror and screen on the optical bench. Hold the mirror so that rays from the sun fall directly upon it. Failing that, hold it so that rays from a candle held at the opposite end of the room fall upon it. Focus the image on the screen. To do this move the screen until
the image is clear and sharply defined. 2. Measure the distance of the image from the vertex of the mirror. Observations 1. What is observed when parallel incident rays are reflected from the mirror? 2. Describe the image obtained when the object is at infinity. 3. What is the distance of the image from the vertex of the mirror? Conclusions 1. What effect does a concave mirror have on light rays incident upon it? 2. Define; principal focus, focal length. 241 Chap. 21 LIGHT Questions 1. Why may a concave mirror be called a converging mirror? 2. Why did we use an infinitely distant object in the above experiment? EXPERIMENT 6 To study the images produced by a concave mirror, (Ref. Sec. IV: 15) Apparatus Optical bench, concave mirror of known focal length, candle, screen, finder. Method 1. Place the candle at more than twice the focal length (/) from the mirror. Locate the image on the screen and state its characteristics. 2. Repeat the above for two or three other positions of the candle as it is gradually moved nearer to the principal focus of the mirror. 3. Place the candle between the principal focus and the mirror. Look into the mirror to see the image. Note its characteristics and locate its position by the method of parallax using the finder. Observations Observation Number Position of Object Position of Image Characteristics of Image Kind Attitude Size 1. 2. 3. Conclusions 1. Where may an object be placed so that a real image of it is produced by a concave mirror? 2. Describe the changes in position and characteristics of the image as the object is gradually moved from infinity to the principal focus of a concave mirror. 3. Describe the position and characteristics of the image when the object is between the principal focus and the mirror. Question Make accurate scale diagrams to locate the images for the above positions of the object. EXPERIMENT 7 To study the images produced by a convex mirror, (Ref. Sec. IV: 16) 242 EXPERIMENTS ON LIGHT Apparatus Optical bench, convex mirror, candle, finder. Method Using the candle at three different positions from the mirror, locate the image each time by the method of parallax, and state its characteristics. Observations Observation Number Position of Object Position of Image Characteristics of Image Kind Attitude Size 1. 2. 3. Conclusions
1. What kind of image is produced by a convex mirror? 2. Describe the position and characteristics of the images produced by a convex mirror for all positions of the object. Questions 1. How would you find the focal length of a convex mirror? 2. Why may such a mirror be called a diverging mirror? 3. Construct a geometric diagram to locate the image of an object produced by a convex mirror. EXPERIMENT 8 To measure the refractive index of glass, (Ref. Sec. IV: 21, 23) Apparatus Rectangular block of plate glass with one pair of opposite edges polished, sheet of paper, tack board, pins, geometrical instruments. M 243 Chap. 21 LIGHT Method 1. Lay the sheet of paper on the tack board. Place the glass block on the sheet of paper. Outline its position carefully. 2. Stick a pin A upright in the paper, near the centre of one edge of the glass and touching it. 3. Stick a second pin B upright in the paper about 2 in. from A so that a line joining the two meets the glass obliquely. 4. Look through the block, line up the images of A and B and insert pin C against the opposite edge of the glass block so that it and the images of A and B appear in a straight line. Mark the position of each pin. 5. Remove the block and pins and draw BA, and AC. Draw the normal MN at A. With centre A describe a circle to cut AB at D and AC at E. From D and E draw perpendiculars DF and EG to the normal MN. 6. Measure the distances DF and EG and calculate the value of DF With a protractor measure the angles of incidence ( Z BAF) and of refraction ( Z CAG). Using a table of sines calculate sin Z i -r- sin Z r. EG. 7. Repeat for several other positions of the pins and arrange your results in the following observation table. Observations Obs. No. DF EG DF/EG Z i Z r sin Z i/sin Z r 1. 2. 3. 4. Average Average Conclusion Define: Index of Refraction. Questions 1. Compare your experimental value with the theoretical value (table p. 199). Calculate your percentage error. 2. Which way does light bend on entering obliquely a different medium of greater optical density? Why? EXPERIMENT 9 To trace the path of light
through a glass plate with parallel sides. (Ref. Sec. IV: 24) 244 EXPERIMENTS ON LIGHT Apparatus Same apparatus as in experiment 8. Method 1. Lay the sheet of paper on the tack board. Place the glass block on the sheet of paper. Outline its position carefully. 2. Stick two pins A and B upright in the paper, about 2 in. apart, so that a line joining them (the incident ray) strikes the glass obliquely. 3. Look through the block, line up the images of A and B and insert pins C and D about 2 in. apart so that they and the images of A and B appear in a straight line. Mark the position of each pin. 4. Remove the block and pins. Join AB and produce it to meet the block at E. Join CD and produce it to meet the block at F. Join EF. On your diagram label the incident, refracted, and emergent rays. 5. Draw the normals at E and F. Measure the angle of incidence at E, and the angle of emergence at F. 6. Repeat the experiment for angles of incidence of different sizes. Observations 1. In what direction relative to the normal does the light ray bend on entering the glass at E and on leaving it at F? 2. Angle of incidence at F = Angle of emergence at F = 1. 2. 3. Conclusions 1. How does the angle of incidence compare with the angle of emer- gence? 245 Chap. 21 LIGHT 2. What relationship exists between the directions of the incident and emergent rays? 3. Describe the path of a light ray through a glass plate with parallel sides. Explanation Explain the observed bending of the light ray on entering and on leaving the glass. Question What factors affect the amount of lateral displacement of the emergent ray? EXPERIMENT 10 To illustrate the apparent change in depth due to refraction of light at a plane surface. (Ref. Sec. IV: 24) Apparatus Tall beaker, two pins, water. r_- Water Real Depth Apparent Depth ^Search Pin S Object Pin O Fig. 21:6 Method 1. Place a pin at the bottom of the beaker and pour in water to a depth of about 15 cm. This pin is the object, O. 2. Hold the search pin, S, horizontally outside the beaker. View from directly above and adjust the position of the search pin until there is
no parallax between it and the image of the object pin. 3. Determine the distance of the object pin, and of the search pin from the surface of the water, thus finding the real and apparent depths. 4. Repeat the experiment using different depths of water. 5. Tabulate your observations and determine the average value for real depth apparent depth. 246 EXPERIMENTS ON LIGHT Real Depth Apparent Depth Real Depth Apparent Depth Observations Observation Number 1. 2. 3. 4. Conclusions 1. Construct a diagram to show the path of the light rays from the immersed object to an observer’s eye. 2. Why is the apparent depth always less than the real depth? 3. Compare the value obtained by dividing the real depth by the appar- ent depth to the index of refraction of water (table, page 199). Questions 1. In step 3 of the method, why must the measurements be made on the outside of the beaker? 2. If the water in the above experiment were replaced with an optically denser liquid, e.g., carbon tetrachloride, what effect would this have on the apparent position of the object? Why? Try the experiment. EXPERIMENT 11 To show deviation produced by refraction through a prism. (Ref. Sec. IV: 25) Apparatus A 60° prism, sheet of paper, tack board, four pins, geometrical instruments. A Fig. 21:7 Method A. Demonstration Experiment—Optical-Disc Method (Sec. IV: 25). B. Student Experiment—Pin Method. 247 Chap. 21 LIGHT 1. Lay the sheet of paper on the tack board. Place the prism on the paper. Outline its position carefully. Label its vertices A, B and C. 2. Stick two pins P and Q upright in the paper about 2 in. apart so that Q is touching the prism, and a line joining them (the incident ray) strikes the surface of the prism, AB, obliquely. 3. Look through the prism on the side AC. Line up the images of P and Q and insert pins R and S about 2 in. apart with R touching the prism, so that they and the images of P and Q appear in a straight line. Mark the position of each pin. 4. Remove the prism and the pins. Join PQ, QR and RS. Label the incident, refracted and emergent rays. 5. Extend PQ
and SR to meet at D. Measure the size of Z D (angle of deviation). 6. Construct the normals at Q and R. Measure the angle of incidence and the angle of emergence. 7. Repeat on separate diagrams for three other angles of incidence, including the special case where the angle of incidence is equal to the angle of emergence. Observations 1. Which way does the light ray bend (a) on entering the prism? (b) on leaving the prism? Angle of Incidence Angle of Deviation Angle of Emergence 2. Obs. No. 1. 2. 3. 4. Conclusions 1. Describe the path of a light ray through a prism. 2. Describe how the angle of deviation varies as the angle of incidence is changed. 3. What is the relationship of the angle of incidence to the angle of emergence when the deviation is a minimum? Questions 1. Draw a diagram showing a ray of light passing through the prism at the position of minimum deviation. 2. What factors affect the amount of deviation produced by a prism? EXPERIMENT 12 To study the action of a convex and a concave lens, and to determine their focal lengths, (Ref. Sec. IV: 28, 29) 248 EXPERIMENTS ON LIGHT Apparatus Optical bench, convex lens, concave lens, candle, screen, finder. [ 'r'^ I I'' Fig. 21:8 Method A. Demonstration Experiment—Optical-Disc Method (Sec. IV: 29). B. Student Experiment—Optical-Bench Method. 1. Mount the convex lens and screen on the optical bench. Hold the lens so that rays of light from the sun, or from a distant candle, fall directly upon it. Focus the image on the screen. 2. Measure the distance of the image from the optical centre of the lens. 3. Repeat using the concave lens. In this case, in order to see the image, it is necessary to look into the lens toward the object. The position of the image can be determined by the method of parallax with the aid of the finder. Observations 1. What is observed when parallel incident rays are refracted through (a) the convex lens, (b) the concave lens? 2. Describe the image obtained when the object is at infinity using (a) the convex lens (b) the concave lens. 3. What is the distance of the image from
the optical centre of the lens? Conclusions 1. What effect do (a) a convex lens, (b) a concave lens, have on light rays incident upon them? 2. Define: principal focus, focal length. Questions 1. What other name may be given to (a) a convex lens, (b) a concave lens? Why? 2. Why did we use an infinitely distant object in the above experiment? EXPERIMENT 13 To study the images produced by a convex lens, (Ref. Sec. IV: 30) 249 Chap. 21 LIGHT Apparatus Optical bench, convex lens of known focal length, candle, screen, finder. Method 1. Place the candle at more than twice the focal length (/) from the lens. Locate the image on the screen and state its characteristics. 2. Repeat the above for two or three other positions of the candle as it is gradually moved nearer to the principal focus of the lens. 3. Place the candle between the principal focus and the lens. Look into the lens to see the image. Note its characteristics and locate its position by the method of parallax using the finder. Observations Observation Number Position of Object Position of Image Characteristics of Image Kind Attitude Size 1. 2. 3. Conclusions 1. Where may an object be placed so that a real image of it is produced by a convex lens? 2. Describe the changes in position and characteristics of the image as the object is gradually moved from infinity to the principal focus of a convex lens. 3. Describe the position and characteristics of the image when the object is between the principal focus and the lens. Question Make accurate scale diagrams to locate the images for the above positions of the object. EXPERIMENT 14 To study the images produced by a concave lens. (Ref. Sec. IV: 31) Apparatus Optical bench, concave lens, candle, finder. Method Using the candle at three different positions from the lens, locate the image each time by the method of parallax, and state its characteristics. Observations Observation Number Position of Object Position of Image Characteristics of Image Kind Attitude Size 1. 2. 2 250 EXPERIMENTS ON LIGHT Conclusions 1. What kind of image is produced by a concave lens? 2. Describe the position and characteristics of the images produced by a concave lens for all positions of the object. Questions 1. How
would you find the focal length of a concave lens? 2. Why may such a lens be called a diverging lens? 3. Construct a geometric diagram to locate the image of an object produced by a concave lens, EXPERIMENT 15 To study the dispersion of white light into the spectrum. (Ref. Sec. IV:36(a) Apparatus Projection lantern, single slit, converging-lens, prism, white cardboard screen. Method Direct a beam of light from the projection lantern on to the slit. Place the converging-lens in the light that diverges from the slit, and focus these rays on the screen at A. Place the prism in the path of the beam and note what happens to the light. Rotate the prism so that the emergent beam sweeps to and fro. Adjust the position of the prism until the emergent beam is as near as possible to A. The prism is now in the position of minimum deviation. Move the screen into the path of the beam and adjust its position until the light which falls on it is in clear focus. Observations 1. What happened to the beam of light on passing through the prism? 2. Name the colours of the spectrum that you see. 3. Which coloured rays are deviated least, and which most, by the prism? 251 Chap. 21 LIGHT Explanation 1. Why is light deviated on passing through the prism? 2. Why are different colours deviated different amounts? 3. Which is deviated the least? Why? Which the most? Why? Conclusions 1. What must white light consist of? 2. What is meant by dispersion of white light? Questions 1. What would be observed if a sensitive heat detector were placed just beyond the red end of the spectrum? Why? 2. What would be observed if a fluorescent material (e.g., anthracene), were placed just beyond the violet end of the spectrum? Why? EXPERIMENT 16 To recombine the colours of the spectrum into white light. (Ref. Sec. IV:36(b) Apparatus As in experiment 15, second prism identical to one used there, second converging lens, Newton’s colour disc, rotating-machine. Method 1. With apparatus arranged as in experiment 15, place the second prism with its refracting edge in the opposite position to that of Note what is first. Move the screen to catch the image. the obtained. 2. With apparatus arranged as
in experiment 15, place the second converging- lens in the spectrum. Move the lens until the image is brought to a focus on the screen. Again note what is observed. 3. Examine Newton’s colour disc. Strongly illuminate it with white light from the projection lantern. Rapidly rotate it. Note the effect obtained. Place on the rotator. Observations Describe carefully what is observed in each part above. Include diagrams. Conclusion How may the colours of the spectrum be combined to form white light? Explanation 1. Why did the reversed prisms and the converging- lens re-form white light? 2. Why did Newton’s disc appear white when rapidly rotated? 252 EXPERIMENTS ON LIGHT Question How could a concave mirror be used to recombine the colour of the spectrum? EXPERIMENT 17 To study the spectra of a few common elements, (Ref. Sec. IV: 39) Apparatus Direct-vision spectroscope, Bunsen burner with monochromatic flame attachment, sodium, calcium and lithium salts; electrical discharge tubes containing neon, nitrogen and hydrogen, induction coil, source of direct current. Method 1. Place a sample of the sodium salt in the attachment on the burner. Light the burner and heat the salt. Observe the flame through the spectroscope. Repeat for the other salts. 2. By means of the induction coil send a high-voltage discharge of electricity through the tube containing neon. Observe the discharge Repeat using the tubes containing the through the spectroscope. other gases. Observations Describe the spectra obtained and compare with those given in Fig. 19:6. Conclusion How is the spectrum of an element obtained? Questions 1. What is meant by spectrum analysis? 2. What are some of its advantages? EXPERIMENT 18 To study colour in natural objects (a) opaque (b) transparent, (Ref. Sec. IV: 40) Apparatus As in experiment 15, red, yellow and blue cardboard screens; red, yellow and blue glass filters. Method Produce a pure spectrum as outlined in experiment 15. 1. Replace the white screen by the coloured screens in turn. Note any change in the appearance of the spectrum each time. 253 Chap. 21 LIGHT 2. With the white screen in place, insert each of the coloured filters in the path of the beam. Note any change in the appearance of the spectrum each time. 3. Repeat 2 using both the yellow
and blue filters in the path of the light beam. Note the colour of the light obtained. 4. Repeat 2 using all three filters (red, yellow and blue) in the path of the beam. Note what is obtained. Observations Describe carefully all that is observed. Represent your observations by means of simple diagrams. Explanation Account for each of the observations. Conclusion What is the cause of colour in (a) opaque (b) transparent objects? Questions 1. An object is viewed in white light and appears red. Why? 2. A blue filter is placed between the source of white light and the same object. What will be the appearance of the object? Why? EXPERIMENT 19 To study the action of the astronomical refracting telescope, (Ref. Sec. IV: 48) Apparatus Optical bench, convex lenses of 20 cm. and 5 cm. focal lengths. Fig. 21:10 Method 1. Place the two convex lenses on the optical bench so that the distance between them is equal to the sum of their focal lengths (25 cm.). Using the convex lens of shorter focal length as the eyepiece and the other as the objective, look through the lenses at distant objects. 254 EXPERIMENTS ON LIGHT 2. Construct two similar scales, P and Q, with divisions about 1 in. apart and place them near each other at the far end of the room. (Similar scales may be drawn on the blackboard if this is preferred.) Look through the telescope at the scale Q with one eye, and at the same time look at scale P with your other eye. Have your partner mark the point on scale P which is level with the uppermost division of Q observed through the telescope. Repeat for the lowest division observed. Compare the number of complete divisions, AB, observed through the telescope with the number of Determine corresponding scale divisions, A^B^, observed directly. the magnifying power of the telescope. Observations 1. What is observed when distant objects are viewed through the telescope? 2. How many complete scale divisions were observed (a) through the telescope? (b) directly? Calculations AB = A^B^ = 1. Determine the magnifying power of the telescope from the above observations. 2. Compare this value to that obtained by dividing the focal length of the objective by the focal length of the eyepiece. Conclusions 1. What is the action of an astronomical telescope? 2. What is the magnifying power of this
however, to be too much in advance of its time and was soon forgotten. For the next hundred and fifty years there was little progress, but in the latter part of the eighteenth century magnetism began to be recognized as the exact science that it has become today. 22:1). V : 2 SOME PROPERTIES OF MAGNETS When an iron bar is stroked with a natural magnet, the iron itself becomes capable of attracting other pieces of iron It has become an artificial or steel. magnet (Fig. this magnet If is brought near to a number of different materials in succession, it is found that only a few of these, called magnetic substances, are attracted. Among these are iron, nickel, cobalt and a few special alloys. The materials which are not attracted are said to be non-magnetic (Chap. 31, Exp. 1). 259 Chap. 22 MAGNETISM AND ELECTRICITY If a bar magnet is rolled in iron filings, the filings are seen to be attracted in large clumps around the ends of the magnet (Fig. These points at which the magnetic force is concentrated are called the poles of the magnet (Chap. 31, Exp. 2). 22:2). Fig. 22:1 Artificial Magnets (a) A Horseshoe Magnet. (b) A Bar Magnet. A magnet which is suspended freely from a non-magnetic stand will always come to rest with its axis along a line running approximately north-south. The same end of the magnet will always point towards the north. This is designated the north-seeking (N-pole) of the Magnetic Force Concentrated ^ near Ends'Clustered Fig. 22:2 Around the Poles of a Bar Magnet. Filings Iron magnet and the other end is the southseeking pole (S-pole) (Chap. 31, Exp. 3). If the N-pole of the suspended magnet is now approached by the N-pole of 260 another magnet, the poles will be observed to move farther apart (Fig. Fig. 22:3 Demonstrating the Law of Magnetism. of the This motion is caused by a 22:3). force, here one of repulsion. When the suspended magnet is S-pole approached by an N-pole of another magnet they will be attracted to each other. From such observations we may conclude that: like magnetic poles repel; unlike magnetic poles attract. This is called the Law of Magnetism (Chap. 31, Exp. 4).
V:3 THE EARTH AS A MAGNET In the previous section it was shown that a suspended magnet always comes to rest along a north-south line. The magnet behaves in this way because the earth itself possesses a magnetic field as if it contained a huge bar magnet lying (Fig. 22:4). nearly parallel to its axis Why is the end of the magnet that points north labelled 6'? The magnetic north pole is located about 1400 miles south of the geographic north pole in the extreme north-central part of Canada. MAGNETISM Sec. V:3 Fig. 22:5 Demonstration Magnetic Compass. consists The modern magnetic compass (Fig. of a magnetized steel 22:5) needle suspended on a point so that it is free to move in a horizontal plane. The N-pole of the compass will point Fig. 22:6 Map of Canada Showing Points of Equal Declination, 1955. 261 Chap. 22 MAGNETISM AND ELECTRICITY always to the earth’s magnetic north pole. The angle between the true north and the direction in which the compass points is called the angle of declination (Fig. 22:6). It is evident that the angle of declination will vary with position on the earth’s surface. A navigator must determine its value from charts in order find true north from the compass to bearing at his position. The declination at Toronto, Ontario, was approximately 7° west in 1955. This indicates that the angle between the lines drawn from Toronto to the geographic north pole and to the magnetic north pole is 7°, and the magnetic line is west of the line to the geographic pole. The magnetic north pole shifts its position slowly westward, and its exact location must be resurveyed frequently in order to correct charts for navigation purposes. V : 4 THE MAGNETIC FIELD compass-needle at a number of positions at varying distances from the magnet and observing the direction in which the needle points. The space surrounding a magnet in which its magnetic influence can be detected is known as the magnetic field of the magnet. in as the century, Magnetic fields were studied by Gilbut bert sixteenth Michael Faraday (1791-1867) showed that they could be best described and interpreted by means of magnetic maps made up of a series of lines known as lines of force. A line of force may be the path that would be defined travelled by a free N-pole if at liberty to move in a magnetic field. By specifying the movement of an N
-pole in our definition we obtain the conventional direction for the lines of force, i.e., from the N-pole of the magnet, which would repel the free N-pole, to the S-pole of the magnet which would attract it. The effect of a magnet is noticeable over a considerable space surrounding it. This can be demonstrated by placing a An effective method of demonstrating the disposition of the lines of force about a magnet is described in chapter 31, Fig. 22:7 The Magnetic Field about (a) A Bar Magnet (b) Unlike Poles (c) Like Poles. 262 MAGNETISM Sec. V:6 experiment 5. Some examples of magnetic maps obtained in this way are shown in Fig. 22 : 7. The properties of lines of force as shown on these maps may be summarized as follows: the 1. Lines of force form closed curves, the magnet, N-pole of leaving proceeding through space to the S-pole, and completing their path through the The apparently loose ends magnet. shown in the diagrams are actually parts of complete lines linking the poles of the magnets. of a magnetized needle that is free to turn in a vertical plane, and a protractor to measure its inclination from the horizontal (Fig. 22:8). The plane of this needle must be adjusted so that it is parallel to the direction indicated by a compass. The instrument will then indicate the direction of the lines of force. At the magnetic poles the needle will repel each other, 2. Lines of force never cross but tend thus spreading to farther and farther apart as they leave the N-pole of the magnet. 3. Lines of force behave like stretched elastic bands, tending to contract and thus to shorten their paths. 4. The concentration of the lines of force determines the strength of the magnetic field at any point. Thus the field is strongest close to the poles of the magnet. The property of that allows magnetic lines of force to pass through it is called permeability. Substances such as soft iron and permalloy, an alloy of nickel and iron, which allow pass through them lines of readily are said to have a high permeability. For this reason these materials are used where a strong magnetic field is desirable as in the electromagnet (Sec. V:50) V:53). galvanometer substance force and (Sec. the to a V ; 5 THE ANGLE OF INCLINATION In section V : 3 the earth was described as possessing a magnetic field of its own. It is the horizontal
component of this field that activates the magnetic compass. The exact direction of the magnetic lines of force may be determined by the use of a dipping needle. This consists Fig. 22:8 Dipping Needle. thus be 90°. stand vertically and the reading on its At the protractor will magnetic equator the needle will be horizontal and the angle of inclination or dip will be 0°. Other locations on the earth’s surface will give readings between these extremes. At Toronto the angle of inclination is about 74°. V:6 INDUCED MAGNETISM An unmagnetized piece of soft iron If, however, will not attract iron filings. we bring it near the pole of a bar magnet, the iron will become a magnet and exhibit powers of attraction. When the bar magnet is removed the soft iron will lose its magnetic properties very rapidly. The iron is said to have been magnetized by induction. If the S-pole of the bar magnet approaches the soft iron it can be shown that the end of the iron 263 Chap. 22 MAGNETISM AND ELECTRICITY A Permanent MagUsed to net Being Separate Metal Sheets. Canadian General Electric nearest the magnet becomes an N-pole and the otlier end becomes an S-pole (Chap. 31, Exp. 6). If a bar of soft iron is held at the angle to the earth’s surface that is indicated by a dipping needle and one end is tapped sharply with a hammer, it can be demonstrated that the iron has become a weak magnet (Chap. 31, Exp. 7 ). Thus we see that even the weak ships, hulls of etc. may of buildings, become magnetized by induction. The magnetic fields from these structures may seriously affect delicate measuring instruments such as watches and com- passes. In order to protect such instruments they are frequently enclosed in a magnetic shield of some highly permeable metal. The lines of force pass through the shielding material more readily than through the space enclosed by it (Chap. 31, Exp. 8), and so the instruments operate free from magnetic disturbance. The effect illustrated in Fig. 22:9. of magnetic shielding is Induced magnetism plays an important part in many of the devices that will be studied in later chapters of this unit. V:7 A THEORY OF MAGNETISM If a piece of iron wire magnetized as in experiment 9, chapter 31, is subjected to continued division and sub-division, each piece will be found to be a small magnet possessing an
the molecules become aligned as shown in Fig. 22: 10b. At the end of the bar last touched by the N-pole of the magnet there will be many S-poles of the molecular magnets and thus it will act as the S-pole of our new magnet. The opposite end, having many molecular N-poles will be the new N-pole. In the central region of the bar the N- and S-poles of the molecules will again neutralize each other so that Fig. 22:11 Keepers (a) on Bar Magnets, (b) on a Horseshoe Magnet. The mutual repulsion of the similar molecular poles at the ends of a magnet tends to push the molecular magnets out 265 Chap. 22 MAGNETISM AND ELECTRICITY of alignment and so slowly to destroy its magnetism. To prevent this, bar magnets are usually stored in pairs with opposite poles adjacent and a piece of soft iron, called a keeper, placed across each end as shown in Fig. 22:11. The keepers become magnetized by induction and their molecules tend to hold those of the magnet in alignment. A horseshoe magnet requires one keeper as indicated. only A material which is readily magnetized but loses its magnetism rapidly, such as soft iron, is used to form temporary magnets used in electromagnets (Sec. V:50). The molecules of such substances are readily rearranged. Materials which have a more stable arrangement of molecules such as steel of aluminum, and alnico, an alloy nickel, and cobalt, are more difficult to magnetize, but tend to retain their magnetic properties much longer. Such substances are used to make the permanent magnets used in telephone receivers, galvanometers and other instruments. V:8 QUESTIONS A 1. (a) What is a natural magnet? (b) What is the common name of a natural magnet? 2. From the following list select those materials which are magnetic and those which nickel, aluminum, wood, rubber, iron, copper, lead, non-magnetic: glass, are cobalt, steel, zinc, tin. 3. 4. 5. 6. (a) State the Law of Magnetism. (b) Explain how, with the aid of a compass-needle, you would determine which end of a magnet is the N-pole. simplest form of (a) Describe the magnetic compass. (b) Explain why the N-pole of the compass points to the magnetic north pole
of the earth. (c) Why doesn’t a compass-needle point to the true north pole? Define angle of declination. (a) Define line of magnetic force. (b) Draw the magnetic field about a bar magnet. (c) State three fundamental characteristics of these lines of force. (a) Define angle of inclination or dip. (b) What would be the angle of inclination at (i) the magnetic north 266 pole, (ii) the magnetic south pole and (iii) the magnetic equator? 7. (a) What is induction? meant by magnetic (b) By means of a labelled diagram show how you could induce magnetism into a nail so that the head is an N-pole. 8. 10. 9. (a) Define magnetic permeability. (b) What is "magnetic shielding”? (c) Where and why would shielding be necessary? such (a) Describe how you could magnetize a steel needle. (b) How could a piece of steel wire be magnetized by a bar magnet without returning the magnet in a wide arc? (a) Outline the theory of magnetism, (b) Use this theory to explain: (i) that a magnet when repeatedly cut gives sections that are magnets also. (ii) polarity of a magnet. (iii) that there is no magnetic power in the centre of a magnet. (iv) that magnetism is lost on heating or jarring a magnet. (v) magnetic induction. (vi) magnetic saturation. MAGNETISM Sec. V:8 (vii) the difference between temporary, and permanent magnets. B 1. A rod of soft iron is held vertically and struck with a hammer. test (a) Describe how you would whether the rod is magnetized. (b) Which end should become an S-pole? (c) Why strike it with a hammer? 2. How could you use a compass-needle to distinguish between a magnet and a magnetic substance? 3. (a) How could the lines of magnetic force of a horseshoe magnet be traced? (b) Show by means of a diagram the pattern that you would expect to see. 4. A steel bar is repeatedly stroked from A to B with the N-pole of a bar magnet. A compass-needle is then placed near the end B of the steel bar. Make a diagram of the steel bar and compass-needle and label
all poles. 5. How would you use a compassneedle to distinguish between three bars similar in shape and appearance if one is brass, the second is unmagnetized iron and the third is a magnet? 6. You are given two iron bars — one magnetized, the other not — and nothing else. Describe carefully how you could determine which is the magnet. 267 CHAPTER 23 ELECTROSTATICS 2500 years ago. However, similar discoveries have been made by everyone early in life. What child has not been fascinated to discover that on a cold dry day the comb which has just straightened his hair will now pick up bits of paper? Who has not been startled by a shock after scuffing across a carpet to touch another person or a metallic object? Materials which have gained the property of attracting small bits of paper and other light objects are said to have an electric charge (Chap. 31, Exp. 12). Substances that do not have this charge are said to Since many non-magnetic be neutral. materials are attracted, it is evident that electric charges differ from magnetism. It has been found by many experiments that whenever two different substances are rubbed together each will become this charge electrically charged. that builds up in gasoline tank trucks as they move along the highways. To prevent sparking, which could cause an explosion, a chain drags behind the truck to allow the charge to leak off gradually. Responsibility for many fires has been traced to charges of static electricity and precautions are necessary in many industrial plants to ensure that sparking does It is not occur. V : 1 1 KINDS OF ELECTRIC CHARGES It is a simple matter to prove that a hard rubber or ebonite rod rubbed with cat’s fur or flannel, or a glass rod rubbed with silk, will become electrically V : 9 INTRODUCTION TO ELECTROSTATICS is attributed Greece, about 600 b.c. Every high-school student is familiar with many devices operated by electricity. However, this is electricity in motion, a comparatively recent scientific development. Early experiments in this field were confined to electricity at rest, or static electricity. The discovery of generally electricity to Thales of Miletus, one of the seven wise men of He learned that amber, a yellowish fossilized resin, when rubbed with a fabric would attract light objects. This knowledge an of for over two thousand years. science From the beginning of the seventeenth century electrical science began to grow, and it is from the early experiments
of such men as Gilbert and Gray in England, du Fay in France, and Franklin in America that many of our fundamental concepts of electricity have arisen. The study of electrostatics has paved the way for advancement in current electricity. remained isolated fact V: 10 ELECTRIC CHARGES As mentioned above, the phenomenon of electric charges was first noted over 268 ELECTROSTATICS Sec. V:12 charged (Sec. V:10). If we charge an ebonite rod in tliis way, suspend it by a stirrup from an insulated stand, and approach it with another charged ebon- Xt-N. Fig. 23:1 Like Charges Repel. ite rod (Fig. 23:1), the suspended rod is repelled. If the suspended ebonite rod is approached by a charged glass rod, attraction will be observed (Chap. 31, Exp. 13). Thus we can see that these introduced the term negative to describe the charge produced on an ebonite rod rubbed with fur or wool, and positive for the charge on a glass rod rubbed with silk. A simple law of electrical charges may now be stated: like charges repel each other; unlike charges attract each other. V: 12 THE ELECTRON THEORY Our knowledge of the structure of matter has made great progress since Experimental the turn of the centuiy. work beyond the scope of this text has led to a concept of the atom far different from that held until 1897. Until that time the atom was thought to be the Since then smallest particle of matter. our concept of the structure of the atom has been constantly changing. For our is convenient to think of the purposes it atom as follows: 1. It may be pictured as a miniature solar system with a central relatively large mass, called the nucleus corresponding to our sun, and a number of smaller objects, called electrons travelling in their orbits about the nucleus much as the planets move around the sun. 2. The nucleus is composed of two kinds of particles: (a) Protons—which are positively charged and are considered to have unit mass. (b) Neutrons—which have no electric charge and have the same mass as the proton. 3. The electrons are negatively charged and are approximately as heavy as a proton. University of Toronto Benjamin Franklin are two charges. In different kinds electric 1750 Benjamin Franklin of 4. Atoms are neutral normally in charge. Therefore we may conclude that in each atom there must be as many electrons moving around the nucleus as there
are protons within the nucleus. 269 Chap. 23 MAGNETISM AND ELECTRICITY Hydrogen Oxygen Neon Magnesium Chlorine Fig. 23:2 Diagrams of Several Atoms— Electrons (•), Protons ( + ), Neutrons (n). 5. There are over one hundred different kinds of atoms known at the Scientists believe that present time. even more will be identified in the near future. The atoms of different elements differ from each other in the numbers of protons and neutrons contained in the nucleus and in the number and arrangements of electrons in their orbits. Some typical diagrams of atoms are shown in Fig. 23:2. An understanding of this theory of atomic structure enables us to explain why an object becomes charged by friction. Tremendous forces are required to separate a proton from the nucleus of an atom. However, it is relatively easy to cause an electron to leave an atom or to move to another atom. When an ebonite rod is rubbed with cat’s fur, electrons are transferred from the fur to the ebonite and the rod becomes negaThe fur, having lost tively charged. electrons, becomes positively charged. Similarly, when a glass rod is rubbed with silk, electrons are transferred from the glass to the silk so that the glass becomes positive and the silk negative. We may now define a positive charge as a deficiency of electrons. A negative charge is a surplus of electrons. A neutral body has equal numbers of protons and electrons. 270 V:13 ELECTROSCOPES Before proceeding further in our discussion of electrostatics it is convenient to study the means by which electric charges may be detected and identified. Instruments used for this purpose are called electroscopes. (a) The Pith Ball Electroscope The simplest form of electroscope consists of two balls of dried elder pith, each about the size of a pea, suspended side by side from an insulated stand by silk threads (Fig. 23:3). When the pith balls are approached by an uncharged object no attraction or repulsion will be noted. When a charged ebonite rod is touched to the pith balls, they will be ELECTROSTATICS Sec. V:13 seen to be attracted, cling to the rod for a moment, and then be violently repelled from it. The pith balls have become negatively charged and they will spring apart due to the repulsion of like charges. The stronger the charge, the greater is the repulsion.
When the charged pith balls are now approached by an object bearing the same kind of charge, they will be repelled from it. If the charge on the object is opposite to that placed on the pith balls, they will be attracted to it (Chap. 31, Exp. 14). ball to the rod which, being positively charged, has a deficiency of electrons. Thus, the pith ball, when charged by contact, receives the same charge as the charging object. (b) The Gold-Leaf Electroscope This instrument, shown in Fig. 23:5 is much more sensitive than that described above. It consists of a piece of These observations may be explained electron the readily by reference The to being rod, negatively theory. charged, has an excess of electrons. Because the rod is charged and the pith balls are not, they are attracted to it. As the pith balls touch the rod some electrons move from the rod to the electroscope. Thus the pith balls become negatively charged and are repelled. This is shown diagrammatically in Fig. 23:4. It is frequently convenient to use an electroscope with only one pith ball as shown for electrostatic experiments. events series of Similarly, the pith ball may be given a positive charge by touching it with a charged glass rod. In this case the electrons will be transferred from the pith Fig. 23:5 Gold-Leaf Electroscope. gold-leaf or thin aluminum-foil attached at its upper edge to a brass plate at the end of a brass rod. This assembly is enclosed in a metal case with glass windows for observation. The rod is in- 271 Chap. 23 MAGNETISM AND ELECTRICITY manner (Sec. V:40, V:77). Substances in which the electrons can not move insulators. A few readily common conductors and insulators are tabulated below. called are V : 15 INDUCED CHARGES Two metal spheres, A and B (Fig. 23:6), supported on insulated stands are placed in contact so that they form a ring causes sulated from the case by a of sulphur, wax, or rubber. The rod generally terminates at the upper end in a knob or flat disc to receive the charge. A negative charge on the electroscope may be obtained by touching the knob with a negatively charged rod (Chap. Electrons will be trans31, Exp. 15). ferred from the charged rod. to the knob, rod, plate and leaf
of the electroscope. The similar charge on the plate and leaf leaf diverges. The extent of this divergence is an indication of the strength of the charge. If the knob is now approached by an object bearing the same kind of charge as that on the electroscope, there will be further divergence of the goldIf, however, the object bears the leaf. opposite charge, the leaf will be seen to fall. When touched by a positively charged object, electrons will leave the electroscope and it will be left with a positive charge. repulsion and the V : 14 CONDUCTORS AND INSULATORS In some materials, mostly metals, the loosely bound orbital electrons are so that they will leave the atom readily. In some other substances the electrons are so tightly bound to their nuclei that their movement is slight. Materials in which electrons can move readily are called conductors (Chap. 31, Exp. 16). Conductors may be solids, liquids, or gases, although liquids and gases conduct electricity in a slightly different single conductor. If a negatively charged ebonite rod is now brought near to A as described in chapter 31, experiment 17, and the surfaces of the spheres are examined for charge by means of a charged electroscope and a proof plane (a small metal disc at the end of an insulating-handle used to transfer charges to an electroscope), it will be found that the surface of A near the ebonite rod has acquired a positive charge. A negative charge will be found on the surface of B remote from the rod. If the ebonite rod is removed and the spheres Good Conductors metals graphite water solutions of acids, bases, and salts Poor Conductors dry wood paper alcohol kerosene pure water Good Insulators hard rubber paraffin wax sulphur mica porcelain dry air 272. ELECTROSTATICS Sec. V:17 will again examined, no charges be This is an example of electrofound. static induction. The charges discovered on the spheres while the charged rod was near are known as induced charges. They are due to the repulsion of electrons from sphere A, which thus becomes positively charged, to sphere B, which thus acquired a negative charge. Induced charges are possible only with conductors since there are no free electrons in insulators to allow the moveIf A and B are separment necessary. ated while the ebonite rod is in position, peiTnanent charges will remain on the spheres (positive on A, negative If the
rod is now removed and on B) the spheres allowed to touch, it will be found that no charge remains on either sphere. We may conclude then, that induced charges are equal. still Exp. 18). The leaf diverges as shown in Fig. 23:7 because electrons are repelled to the plate and leaf. Keeping the charged rod near, touch the knob with a finger, that is, “ground” it. The leaf will fall as electrons are repelled from it to “ground”. Next, remove your finger, and then the charged rod. The leaf will diverge again. The remaining electrons are distributed over the electroscope which is left with a deficiency of electrons and thus a positive charge. In order to give the electroscope a negative charge the above procedure must be followed positively charged rod. This method is illustrated Students are advised to in Fig. 23:8. draw the diagrams and make the necessary explanations bearing in mind that “ground” acts a extra source using of as a electrons. V:16 CHARGING BY INDUCTION V: 17 THE ELECTROPHORUS Approach, but do not touch, the knob of a gold-leaf electroscope with a negatively charged ebonite rod (Chap. 31, About 1775 Volta invented the simplest form of machine to produce electric charges by induction, called the electro3) Ground ( 4 ) (5) Fig. 23:7 Charging Gold-Leaf Electroscope Positively by Induction. (1) Uncharged electroscope. (2) Approach rod (— ). with charged ebonite (3) Touch with finger (ground) (4) Remove finger (5) Remove charged rod. 273 Chap. 23 MAGNETISM AND ELECTRICITY Fig. 23:8 Charging Gold-Leaf Electroscope Negatively by Induction. (1) Uncharged electroscope (2) Approach with charged glass rod ( + ) (3) Touch with finger (ground) (4) Remove finger (5) Remove charged rod It consists of a hard rubber or phorus. ebonite cake and a separate metal disc provided with an insulating handle. The ebonite cake is charged negatively by rubbing with fur. The metal disc is then placed on it and touched with a finger. If the disc is then removed by means of the insulating handle it will be found to possess a relatively strong positive charge. The disc has been charged by induction. In order to explain this
is little danger from the discharge because of the small quan- tity of electricity involved. Canadian Laboratory Supplies Ltd. 275 Chap. 23 MAGNETISM AND ELECTRICITY 1. In conductor (a) the leaves of the electroscope show the same divergence matter what part no is touched by the proof plane. 2. In conductor (b) the divergence proves to be a little greater from tests at the ends than at the centre. 3. In conductor (c) the divergence is much greater from tests at the more pointed parts of the conductor than elsewhere. From these tests we may conclude that the charge on a conductor tends to be concentrated at the more pointed parts of the surface. V : 20 LIGHTNING-RODS About the middle of the eighteenth century Benjamin Franklin demonstrated in his classic kite experiment that thunder-clouds carry electrical charges and that lightning is an electrical discharge clouds and objects on the earth. spark between clouds, or or If a metallic point is connected to one of the discharge knobs of a Wims- V: 19 DISTRIBUTION OF CHARGES The location of charges on a charged body may be demonstrated as in chap31, experiment 19A, using Biot's ter Spheres shown in Fig. 23:11. The apparatus consists of an insulated metal over which two tightly-fitting sphere can metal hemispheres be insulated placed to cover it completely. A charge is given to the sphere and then the tightly over it. hemispheres are fitted When the hemispheres are removed and tested using a proof plane and electroscope, each will be found to possess a charge, while the sphere is found to have lost its charge. The charge, then, must have passed to the hemispheres as they formed the outer surface of the sphere. Charges reside only on the outer surface of a charged conductor. To determine how the charge is distributed over the surface of a charged conductor we can charge several insulated conductors of different shapes as described in chapter 31, experiment 19B. On investigation with a proof plane and electroscope the following observations are made: 276 Fig. 23:12 Action of Points hurst machine, as shown in Fig. 23:12, the streaming of charge away from the point is sufficient to blow aside the ELECTROSTATICS Sec. V:21 flame of a small candle (Chap. 31, Exp. 20). The action of points is as if the point produces a self-discharging action, the charge on the conductor streaming away from it as
an “electric wind”. Franklin made use of this action of points as he designed the lightning-rod to protect buildings against the dangers of lightning. As a charged cloud passes its ning with occurs over the earth it induces the opposite charge on objects below. If the charge becomes great enough a flash of lightaccompanying thunder, a shock-wave, caused by the sudden and violent expansion of the air heated by the discharge. The rods are the induced charge so designed escapes from the sharp points and so an accumulation of charge is prevented. If the lightning does strike the rods, a good that conductor leads the electricity safely to ground through a metal rod deeply buried in the damp ground near the building (Fig. 23:13). V : 21 QUESTIONS 1. 2. (a) What is the meaning of static electricity? (b) How is it produced? (c) How is it detected? (a) Name two kinds of static electricity. How is each produced? (b) How would you prove that there are two kinds? (c) State the law for electrical charges. 3. (a) Describe in point form our modern concept of the structure of an atom. (b) In terms of the electron theory, what is (i) a positively charged, (ii) a negatively charged, (iii) a neutral body? (c) Why does (i) ebonite become 5. (ii) glass become negative when rubbed with wool, when rubbed with silk? What is the electrical condition of the wool and silk afterward? positive 4. (a) What are the purposes of electroscopes? (b) Describe and explain what occurs when (i) a positively charged, (ii) a negatively charged object Is brought up to an uncharged pith ball electro- scope. (c) How would you use it to identify an unknown charge? the (a) Describe the gold-leaf electroscope and state the purpose of each part. structure of 277 Chap. 23 MAGNETISM AND ELECTRICITY 8. Describe, using a series of diagrams to illustrate your answer, how to charge a gold-leaf electroscope (a) negatively by induction. positively, (b) 9. Explain the following: (a) the metal disc of an electrophorus can be repeatedly charged without recharging the ebonite cake. (b) the purpose of the Wimshurst machine. (c) electrical charges reside on the 10. outside of a conductor.
(d) lightning-rods are sharply pointed. (e) lightning-rods are connected by a good conductor to ground. A positively charged cloud hovers over a tall church spire. What will be the resulting electrical condition of the spire? What will happen if a large enough charge accumulates on the cloud? 6. 7. (b) Explain how to charge it positively, (ii) negatively by contact. (c) How would you use it to identify an unknown charge? (i) (a) What is a good conductor of electrical charges? Give examples. (b) What is an insulator of electricity? Give examples. (c) How could you use a gold-leaf electroscope to show that iron is a better conductor than wax? (a) What is meant by electrostatic induction? (b) You have a charged glass rod and two metal spheres mounted on insulated stands. Describe how you would charge one sphere negatively, and the other positively, by electro- static induction. (c) How would you verify that the spheres were oppositely charged? 278 1 ^. CHAPTER 24 ELECTRIC CURRENT V:22 INTRODUCTION In chapter 23 it was shown that electrons moved between the terminals of the Wimshurst machine and that lightning is actually a movement of electrons between earth and charged clouds. Such movement of electrons is called an electric current. In the eighteenth century Luigi Galvani, an Italian physiologist, discovered that a freshly dissected frog’s leg showed violent muscular contractions when touched by two dissimilar metals. He erroneously attributed this property to the frog, and it remained for Alessandro Volta, an Italian professor of physics, to demonstrate a short time later that the frog’s leg had acted only as a sensitive detector of electricity which had been produced by contact with the dissimilar metals. Volta showed that this electricity was identical with that produced by frictional means (Sec. V:10). From this beginning he constructed the first source of continuous electric current, the voltaic cell (Sec. V:23). From the time of of Volta’s works in 1800, there has been continuous progress in the field of electricity. The sections that follow will publication help to give you an understanding of the fundamentals of electricity that mean so much in our modern way of life. V:23 THE VOLTAIC CELL Every high-school student is familiar with the tiny dry cell that is used to operate a flashlight and the larger
storage battery used to start a car; these are just two modern forms of the voltaic cell. A voltaic cell consists of two dissimilar materials immersed in a solution of an acid, called the base, or salt, electrolyte. voltaic The simplest form of cell consists of a copper plate and a zinc plate placed in a vessel containing dilute (Chap. 31, Exp. 21). sulphuric acid As a result of the chemical action in the cell the copper plate becomes posiand plate negatively charged. If the plates are charged tively zinc the i—O— 1 Dilute Sulphuric Acid Flashlight Bulb 1 ^. 11111 1 1 11 1111111 'HWT'Copper N. 1 111 II Zinc - Fig. 24:1 Diagram of Simple Voltaic Cell. 279 Chap. 24 MAGNETISM AND ELECTRICITY then connected by a conductor (Fig. 24:1) the potential difference between them will cause electrons to flow from the zinc to the copper. The circuit is As completed through the electrolyte. the current flows, hydrogen is deposited on the copper plate and zinc sulphate dissolves in the electrolyte as the zinc is gradually used up. The potential difference between the plates is approximately 1.1 volts. This P.D. is independent of the size of the plates used, but In all varies with the materials used. such cells chemical energy is transformed into electrical energy. V : 24 DEFECTS OF THE VOLTAIC CELL 1. Polarization If a small flashlight bulb is connected in the circuit of a voltaic cell it will glow brightly for a short time and then fade gradually until no light is seen (Chap 31, Exp. 21). It is apparent that the current delivered by the cell has decreased. This effect is caused by po- METAL CAP, with washer to insulate the cap from the metal cover. EXPANSION SPACE, for expansion of cell contents during use. as the ZINC CAN serves as the negative plate and at the same time container for the cell. ELECTROLYTIC PASTE sal-ammoniac containing and zinc This reacts with the zinc making it electro-negative and producing hydrogen which moves toward the carbon rod. chloride. larization, which is the accumulation of bubbles of hydrogen on the positive plate. The hydrogen deters the acid from reaching the plate and serves as an insulator preventing further transfer of electrons. To restore a polarized cell the bubbles may
and shapes have been made to fill many needs. They are widely used for flashlights, portable radios, telephones, hearand many other ing devices used by the armed forces and industry. lanterns, aids, V:26 THE ELECTRIC CIRCUIT The flow of electrons in a wire is so similar to the flow of water in a pipe a comparison may be made as that As the cell is used the zinc becomes follows: The Water System The Electric Circuit 1. Water current is the flow of water through the system. 1. Electric current is the flow of electrons through the wires. 2. Water flows through a closed system of pipes between source and user. 3. The quantity of water in a system is measured in gallons or similar units. 4. The current of water is measured in gallons moving through the pipe in a unit of time. 5. Water current is reduced by the friction between the water and the pipes. 2. Electrons flow through a closed path of wires called a circuit. 3. The quantity of electricity is measured in coulombs. A coulomb is equal to approximately 6.28 billion billion electrons. 4. The electric current is measured in amperes. An ampere is the current when one coulomb passes a point in the circuit in 1 second. 5. Electric current is decreased by the resistance of the conductor. The unit of resistance is the ohm. 281 : Chap. 24 MAGNETISM AND ELECTRICITY The Water System 6. Water is driven through the pipes by pressure which is measured in pounds per square inch or related units. Pressure is provided by increasing the potential energy of the water by high tanks. The force so created pushes the water to its destination although the water pressure decreases as the length of pumping into it pipe increases. The Electric Circuit 6. Electrons move through a circuit because of a difference in electrical pressures or potential difference (P.D.) between points in the wire. This potential difference is measured in volts. The pressure difference is maintained by the use of batteries or cells which provide a source of electrons by means of the transformation of chemical energy. This potential difference is the electromotive force necessary to move the electrons through the wire. Resistance in the circuit causes a lowering of potential ence between points the conductor. This is referred to as a voltage drop. differ- in The units of electricity in common use and their symbols are sum- marized below for convenient reference (b) Current of electricity (a) Quantity of electricity (Q) —
-unit is the coulomb (/) — unit is the ampere {V ) — unit is the volt (R) — unit is the ohm Potential difference (d) Resistance (c) Smaller or larger units are obtained by using submultiples or multiples of these as: 1 milliampere = 1/1000 ampere 1 microampere = 1/1, 000, 000 ampere 1 millivolt = 1/1000 volt 1 megohm V : 27 ELECTRIC CURRENT AND ELECTRON FLOW Electric current has been defined as the flow of electrons through the wires of a circuit (Sec. V:26). From the beginning of electrical theory, the current has been considered to flow, as is the case with water, from the place of high potential to the place of lower potential. Early scientists considered the positive side of a source of electricity to be at 282 1 microvolt 1 microhm 1 kilovolt = 1,000,000 ohms etc. = 1/1,000,000 volt = 1/1,000,000 ohm = 1,000 volts a higher potential than the negative side. Thus, the convention that electric current flows from positive to negative came into common use. We now know that the negative side of a source has a surplus of electrons and the positive side a deficiency of a electrons fundamental law of nature, electrons move from where there are more to where there are fewer. Electrons, there- (Sec. V:12). Following fore, actually move from negative to (b) Parallel Circuit ELECTRIC CURRENT Sec. V:29 positive. In all work on electronics, including radio, it is necessary to refer to electron movement in order to understand the operation of modern devices. However, in most other electrical work, unless definitely specified, references have been confined in the past to the conventional current flow, i.e., positive to negative. In most modern writings, including this text, all references are to the electron flow. No difficulty need arise if the difference between current flow and electron flow is recognized. V : 28 TYPES OF CIRCUITS Two main types of connection are in common use in electric circuits and all others are merely combinations of these. (a) Series Circuit In this arrangement the current goes from one terminal of the source to one terminal of the first appliance. On passing through this, it flows to the next and the next until it reaches the other terminal of the source (Fig. 24:3
). All In the parallel or shunt type of connection the conductor from the positive terminal of the source is connected to one terminal of each appliance and the negative terminal of the source is connected to the other terminal of each Electron Flow 4- Battery Appliance = © (I) (£) (p Fig. 24:4 Parallel Circuit. appliance (Fig. 24:4). This is typical of wiring circuits used in your home. Each appliance receives current independently from the others and thus a break in one does not interfere with the operation of the rest. V:29 ARRANGEMENT OF CELLS (a) Series If the resistance in a circuit is so great that the P.D. of one cell is not sufficient to provide the required current, a number of cells may be connected in series. The positive terminal of the is connected to the negative of the second, the positive of the second cell first the current must pass through each appliance, causing a voltage drop (Sec. V:26) in the circuit. A break in any part of the circuit will stop all flow of current. Series circuits are frequently found in Christmas-tree lights, but are seldom used for other purposes. Fig. 24:5 Battery of Cells Connected in Series. 283 Chap. 24 MAGNETISM AND ELECTRICITY to the negative of the third, etc. Such an arrangrnent of two or more dry cells is called a battery. When cells are connected in series the total P.D. is equal to the sum of the voltages of the indiradio vidual B-battery, for example, is composed of thirty dry cells connected in series (Fig. cells. A forty-five volt 24:5). (b) Parallel If the resistance in a circuit is low and a large current is to be used, dry cells are connected in parallel. All the positive and negative terminals are connected as shown in Fig. 24:6. The P.D. of such a battery remains the same as that of a single cell. Since the current is provided equally by all cells the parallel arrangement gives a large current for a relatively long period of time. V : 30 SWITCHES Just as taps are inserted in a pipe line to stop the flow of water, so switches are used to interrupt the flow of electric current in a circuit. These are devices which break or complete the conducting path. Many types of switches are in common use, but only two will be described here. erally of the type shown in
Fig. 24:7a. Wall switches are smaller variations of the same type. (b) Push Button Switch This familiar type is shown in Fig. 24:7b. It is used to control low-voltage Fig. 24:7 Switches (a) Main House Switch (b) Push Button Switch circuits in which the current is required for short intervals only. Electric doorbells, signal buzzers, etc. make use of this type of switch. at this their description Many newer types of switches have been devised for specific purposes, but the scope of this text does not allow The interested student will find information on mercury switches, automatic circuit breakers, and special switching arrangements such as those used to control a stairway light from either upstairs or downstairs in any good wiring handbook. time. V:31 USE OF SYMBOLS (a) Knife Switch Modifications of the common knife switch are used to control many household circuits. The main switch is gen- In order to represent the many pieces of equipment encountered in electrical drawings and circuit diagrams, a number of conventional symbols have been de- 284 ELECTRIC CURRENT Sec. V:31 vised. A few of the most common symbols are introduced at this point so that the student may use them in the work which follows. SOURCES OF •potential DIFFERENCES + Cell —wwvw Fixed Resistors WIRING I Battery (Cells in Series) RESISTORS AWWW- L T T T Battery (Cells in Parallel) METERS Wires Joined Wires Crossing Not Joined RADIO Voltmeter Ammeter Fig. 24:8 Common Electrical Symbols 285 Chap. 24 V : 32 MAGNETISM AND ELECTRICITY QUESTIONS 5. Define the following: electric circuit, ampere, coulomb, electrical resistance, potential difference. 6. (a) Name the two principal types of circuits and define each. electrical (b) State the advantages and disadvantages of lights each way. (c) Make a diagram showing three lights connected in each of these ways. connecting electric 7. (a) Distinguish between the arrangement of cells in series and in parallel. (b) What is the purpose of each of these arrangements? (c) What would be the difference of three dry cells connected potential (I) in series (ii) in parallel? 8. Make a diagram of a circuit containing a cell, a fixed resistor, two wires joined, two wires crossing but not joined, a fuse
, a lamp, a switch. 1. 2. 3. (a) What is an electric current? (b) How is an electric current produced? (a) Make a diagram of a simple voltaic cell. Mark the direction of the electric current (electron flow). (b) What determines the voltage of such a cell? (c) What transformation of energy takes place in a voltaic cell? (a) What are defects in a voltaic cell? (b) How are the defects overcome? two the principal 4. (a) Make a labelled diagram of a dry cell. (b) State the purpose of each struc- ture or material labelled in part (a). (c) What is the voltage of a dry cell? (d) Why are different sizes? dry cells made in 286 ; CHAPTER 25 OHM’S LAW AND RESISTANCE V:33 OHM'S lAW relationship The between current strength, potential difference, and resistance of the circuit is of the utmost importance in practical electricity (Chap. In such an experiment 31, Exp. 22). the potential difference across the revaried by connecting sistance different numbers of dry cells coil is Dry Cells ment is shown in Fig. 25:1. Let us consider some sample results of such an experiment No. of Cells Galvanometer deflection No. of Cells (divisions) Deflection 1 2 3 4 5 4.9 9.8 14.8 19.7 24.5 0.204 0.204 0.203 0.203 0.205 Within the limits of experimental error. Number of cells in the Galvanometer deflection And, since the P.D. across the resistance coil varies directly as the number of cells used, and the galvanometer deflection is proportional to the current through the coil, we have Potential Difference ~ a constant Current Strength or Current Strength is proportional to Potential Difference The strength current circuit. flowing through the coil is gauged by the deflection of a galvanometer needle ( Sec. V : 53 ). A circuit for this arrange- the of in the This relationship was first investigated by nineteenth early George Simon Ohm. The results of his work, published in 1826, are embodied in the law bearing his name. Ohm’s Law may be stated as follows: century The current through a given conductor is proportional to the potential difference between its ends. It must, however, be emphasized that 287. : Chap.
25 MAGNETISM AND ELECTRICITY this law is true only if the temperature remains constant (Sec. V:34). The value of the constant derived above is known as its resistance {R) The unit of resistance is the ohm which may be defined on the basis of Ohm’s Law as being the resistance of a conductor which permits a current of one ampere to flow when a potential difference of one volt is applied across it. Ohm’s Law may be written, then, as Potential Difference „ = Resistance. or = Ohms Current Volts Amperes V I This formula may be rearranged to read V = IR or I = V/R All of these forms will be found useful in numerical work. Problem examples are given in sec- tion V:36. FACTORS AFFECTING >f:34 RESISTANCE The resistance of a conductor depends on four main factors; (a) Length—The resistance of a con- ductor varies directly as its length i.e., twice the length gives twice the resistance; half the length gives half the resistance; etc. (b) Cross-section—The resistance of a conductor varies inversely as the area of twice the cross-sectional area gives half the cross-section i.e., its resistance; half the cross-sectional area gives twice the resistance; etc. (c) Temperature—In most metals an increase in temperature causes an inin some crease resistance, but in 288 substances such as glass, carbon and electrolytes an increase in temperature causes a decrease in resistance. (d) Material—Materials differ widely in their resistances. Good conductors such as copper and aluminum have very low resistances. Poor conductors such as nichrome and manganin have much higher resistances. Good insulators, such as glass, mica, etc., have very high resistances. Relative Resistances of Some Common Materials (in ohm-cms at 20°C.) Aluminum Copper Iron Mercury Nichrome Platinum Silver Tungsten X 10-6 2.83 1.72 10.0 95.8 100 10.0 1.63 5.51 V : 35 RESISTORS IN SERIES AND IN PARALLEL The potential difference which causes the current to flow between the ends of a resistor is frequently called the voltage drop across the resistor. The value of a voltage drop (F) may be readily calculated by using Ohm’s Law. (a) Resistors in
NETISM AND ELECTRICITY circuit (b) the current in the circuit (c) the voltage drop across each lamp. fi = 30 ohms t2 = 20 ohms (a) (b) ri = 2)0 ohms 72 = 20 ohms R =? v = no volts /? nr 50 ohms 1 =? / = 2.2 amp. 7i = 30 ohms rg rr 20 ohms 1^ V =110 volts H'R = Ti + 72 (series connection) i? = 30 + 20 = 50 total resistance in circuit = 50 ohms I = — (Ohm’s Law) R 7 = 112 = 22 50 current in the circuit = 2.2 amp. Vi — hi (Ohm’s Law) vi = 2.2 X 30 = 66 voltage drop across Li = 66 volts V2 = Ir2.\v2 = 2.2 X 20 = 44 voltage drop across = 44 volts. Example 3 If two lamps Li, Lg, of resistance 30 ohms and 20 ohms are connected in parallel in a 110 volt circuit, determine (a) the effective resistance of the circuit (b) the current through each lamp. 290 OHM’S LAW AND RESISTANCE Sec. V:37 :a) Ti — 30 ohms r =20 ohms R =? (b) = 110 volts = 30 ohms = 20 ohms _ p —? OF RESISTORS Ti 72 — = — + — (parallel connection) R 1 _ 1 “so R=\2 effective resistance of the circuit =12 ohms. 1 _ 5 _ 1 20 ~~60 ~ 12 V I j =z — (Ohm’s Law) ri 110 II 11 CO 30 current through Li — 3.7 amp. rz.•./5 = — = 5.5 current through Lg = 5.5 amp. 20 be made from special constantan or manganin (alloys of copper and nickel), having an accuracy within 1 %. These are in general use laboratory work and measuring- for instruments. A number of coils of fixed resistance are frequently arranged together in a Resistors are used primarily to control current and potential difference in eleccircuits. They are constructed in tric many forms and sizes varying from those which have resistances of only a fraction of an ohm, as used in some measuring instruments, to those having resistances of
many megohms as found in radio receivers. In general, however, resistors may be classified or variable. either fixed as (a) Fixed Resistors These may be constructed of short lengths of metal strip for very low resistances. Carbon or wire coils will provide higher resistances. Carbon resistors are frequently used in radios and other equipment in which some variation in resistance is permissible since such resistors may have an error tolerance of up to 20%. Wire-wound resistors may Fig. 25:4 Section of Resistance Box. Details of construction resistance box. are shown in Fig. 25:4. The ends of the 291 Chap. 25 MAGNETISM AND ELECTRICITY the two (Chap. 31, Exp. 23 and 24) which follow: (a) Voltmeter—Ammeter Method The unknown resistance, R, is connected in the circuit shown in Fig. 25:6. The rheostat is adjusted until the amme(Sec. V:54) records any suitable ter coils are attached to brass blocks on the top of the box and the current passes through the blocks when the shortingplugs are placed in position. Pulling out the plug puts the resistor below it into the circuit. Such a box provides a large range of standardized resistors for laboratory use. To avoid errors in using the plugs must be a resistance box, Plugs and sockets must inserted firmly. be kept clean at all times. (h) Variable Resistors (Rheostats) Such resistors are usually continuously variable between certain limits. A common form of rheostat is shown in Fig. It consists of a number of turns 25:5. Fig. 25:6 for Determining Voltmeter-Ammeter Method the Value of an Unknown Resistance. value for the current passing through the resistor. The voltmeter (Sec. V:54) across the resistor indicates the potential difference between the ends of the resistor. From this information the resistance may be calculated by using Ohm’s Law. V = LToUs R=? Example = J.•./e = l^ = 4 3.'. The resistance is 4 ohms. (b) Substitution Method The unknown resistance may be connected in a circuit as shown in Fig. 25:7. The rheostat is then adjusted until a large deflection is shown on the ammeter, or galvanometer (Sec. V:53). The meter reading is noted and the un- Fig. 25
:5 Rheostat. of wire wound on a porcelain tube. Above the coil is supported a metal bar along which moves a metal spring which can make contact at any turn of the coil. Connections are made to the end of the bar and to the end of the coil to enable the resistance in the circuit to be readily adjustable by moving the spring. Variable resistors such as this are of various sizes and shapes and are used in radio volume controls, for dimmer lights in theatres, starter boxes for heavy electric motors, etc. V:38 METHODS OF MEASURING RESISTANCE Although there are several methods the scope of of measuring resistance, this text permits the discussion of only 292 OHM’S LAW AND RESISTANCE Sec. V:39 known resistance is replaced by a rePlugs are removed until sistance box. the meter reading is the same as before. The resistance of the box is now equal to the unknown resistance. WAW\/\ Rheostat Substitution Fig. 25:7 for Determining the Value of an Unknown Resistance. Method Battery Galvanometer O Ammeter or —WWW Unknown Resistance or Resistance Box V : 39 QUESTIONS 1. 2. (a) State Ohm’s Law and explain how it may be determined. (b) Calculate resistance the of a light bulb which carries a current of 5.0 amperes when connected in a 110 volt circuit. (a) In terms of Ohm's Law define: ohm, volt, ampere. (b) What weakness in these definitions is apparent? 3. (a) Explain electrical resistance. (b) List four factors affecting re- sistance. State the effect of each. 4. (a) What is meant by voltage drop across a resistor? (b) What is the effect on the total resistance of connecting a number of resistors (i) in series, (ii) in paral- lel? If two lamps of resistance 50 (c) ohms and 40 ohms are connected in series in a 110 volt circuit calculate (i) the total resistance of the lamps (ii) the current in the circuit (iii) the voltage drop across each lamp. (d) If two lamps of resistance 20 ohms and 40 ohms are connected in parallel in a 110 volt circuit, determine (i) the effective resistance of the circuit. (ii) the current through each lamp. 5. 6. (a)
Describe a resistance box and a rheostat. State the purposes of each, (b) What is the effect of removing a plug from a resistance box? (a) Describe two methods for finding the resistance of a conductor. (b) In an electrical circuit, the ammeter reading is 5.5 amperes and the is 77 volts. potential What is the resistance? difference B 1. What is the resistance of a flashlight bulb which carries a current of 0.50 ampere when connected in series with a 6.0 volt battery? 2. The resistance of a conductor is 25 ohms and it carries a current of 8.5 amperes. What is the potential difference? 3. How much current does a 36 ohm resistance draw when operated on a 120 volt line? 4. (a) What current flows through a 99.5 ohm resistance connected in series with a 1 2 volt battery having an internal resistance of 0.50 ohm? (b) What is the voltage drop across the resistance and across the battery? (a) What is the electric toaster which passes a current of 5.0 amperes when connected in alio volt circuit? (b) What resistance must be placed resistance of an 5. 293 Chap. 25 MAGNETISM AND ELECTRICITY in series with the toaster to lower the current to 4.0 amperes? ference of 20 volts is applied between points A and B. 6. Eight lamps, each having a resistance of 330 ohms, are connected in parallel in the 110 volt circuit. Calculate (a) the effective resistance of the circuit. (b) the current in each lamp in the circuit. (c) the total current in the circuit. 7. A battery of resistance 0.10 ohm is connected in series with an ammeter of resistance 0.5 ohm. The ammeter registers 1 0 amperes. When a resistance is placed in series with the ammeter the current drops to 4 amperes. (a) Draw a diagram of the circuit described. (b) Find the voltage of the battery. (c) Find the value of the added resistance. 8. The difference of potential between the ends of a certain resistance coil when a current of 0.36 ampere is passed through is 1.2 volts. What resistance must be connected in parallel with the coil so that, with the same total current, the difference of potential will be only 1.0 volt?
6 ohm the total (a) Calculate resistance between A and B when the switch is closed. (b) Find the current in the 6 ohm resistance with switch open. (c) Find the current in the 1 2 ohm resistance with switch closed. 10. A cell with a potential difference of 2 volts and negligible resistance sends a current through two resistances of 6 ohms and 9 ohms connected in parallel. In series with the cell is a third resistance of 2 ohms. Calculate the current in the 6 ohm resis- tance. 11. A current of 4.0 amperes is passed through a resistance of 2.0 ohms in series with a parallel combination of 4.0 ohms and 6.0 ohms. Calculate (a) the current in each of the parallel resistances. 9. Three resistances are connected as shown in the diagram and a potential dif- (b) the potential difference across the whole circuit. 294 CHAPTER 26 CHEMICAL EFFECTS OF ELECTRIC CURRENT reason that one can receive a severe electric shock while standing in water or on a damp floor. V : 40 ELECTROLYSIS others All chemical compounds are composed of two or more elements. The elements are composed of atoms as described in Section V:12. Frequently when atoms unite, electrons are transferred from one kind of atom to the other. The atoms electrons become charged which lose positively and the negatively. These charged particles are called ions. The oppositely charged ions attract each other to form ion-pairs. However, the total number of positive and negative charges has not been altered, so that the ion-pairs formed are neutral. When substances formed in this way are dissolved in water, some of these particles and separate dissociate negative ions. Compounds which form ions in solution are capable of carrying electric current and are called electrolytes. Examples of good electrolytes are solutions of acids bases and salts. Many other substances do not ionize when in solution and so do not conduct electricity. These are classed as non-electrolytes. Sugar, alcohol and distilled water are examples of these. Ordinary water salts which usually contains dissolved make it a weak electrolyte. It is for this positive into the water, decomposition of Shortly after the discovery of current electricity by Galvani and the construction of the first voltaic cells, experimenters like Sir Humphrey Davy of England and Svante Arrhenius of Sweden investigated
the decomposition of water by electricity, or as we speak of it now, the electrolysis of water. Davy showed that the in volume of hydrogen produced is double His most striking disthat of oxygen. coveries were the breaking apart by electricity of the alkalis, caustic soda and caustic potash. Arrhenius explained these phenomena by his theory of ionization which assumes that in solutions of electrolytes there is at least a partial dissociation of the dissolved substances into It was not until 1834 that separate ions. Faraday introduced the term anode for the positive plate and cathode for the negative plate cell (Fig. 26:1). The negatively charged ions which are attracted to the anode became known as anions, and the positively charged ions which are attracted to the cathode as cations. When compounds dissociate in solution, metals and hydrogen form cations while non-metals radicals become and in an electrolytic chemical most anions. A typical electrolytic cell consists of two conducting-plates or electrodes immersed in an electrolyte. The anode is 295 Chap. 26 MAGNETISM AND ELECTRICITY the negative connected to the positive terminal of a battery or generator and becomes positively charged while the cathode is conterminal and nected to becomes negatively charged. Anions will move to the anode where they give up their surplus electrons, are neutralized, and released as neutral atoms. These electrons flow from the anode, through the connecting wire to the battery terminal. At the same time cations move to the cathode where they receive electrons and became neutral atoms. Electrons move from the negative battery terminal to the cathode to replenish the to the positive terminal of the battery. The electrolyte is decomposed by the electric current. This process is known as electrolysis. V : 41 ELECTROLYSIS OF WATER Water may be decomposed readily in a simple electrolytic cell (Fig. 26:1), or in the HoflFman water voltameter (Fig. 26:2), by the passage of a direct current through it (Chap. 31, Exp. 25). Fig. 26:2 Hoffman Water Voltameter. A small amount of sulphuric acid (about 10% of the total volume) is added to the water to make it a better electrolyte. The anode and cathode are made of platinum which is unaffected by the electrolyte and is a good conductor of electricity. In solution the acid is highly diss
ociated into positive hydrogen ions (H"^) and negative sulphate ions (S04““). H2S04^2H^ + SO4-- The water is slightly dissociated into positive hydrogen ions and negative hydroxyl ions (OH“) : H 2O + OH-. Fig. 26:1 Electrolytic Cell as Used in the Electrolysis of Water. supply. Thus we have electrons moving from the negative battery terminal to the cathode, through the electrolyte by way of the ions to the anode, and back 296. CHEMICAL EFFECTS OF ELECTRIC CURRENT Sec. V:42 When the voltage is applied to the electrodes the following reactions occur: within the electrolyte completes the circuit (Sec. V:40) At the Cathode 1. The positive hydrogen ions are attracted to the negative cathode. 2. Each hydrogen ion is neutralized by gaining an electron from the cathode and becomes a hydrogen atom: + le-»H° 3. The hydrogen atoms immediately combine in pairs to form molecules of hydrogen gas which escape as bubbles: H° + H° ^ H 2. At the Anode 1. The negative sulphate and hydroxyl ions are attracted to the positive anode. 2. The hydroxyl ions are discharged in preference to the sulphate ions. Each hydroxyl ion gives up an electron to the anode to become a neutral hydroxyl group. OH--le-^OH° 3. Pairs of hydroxyl groups then combine to form water and an atom of oxygen. pairs OH° + OH° ^ H 2O + 0 ° 4. The oxygen atoms immediately comto form molecules of bine in oxygen ’gas which escape as bubbles. 0° + 0° ^ O2 As the ions are discharged more water dissociates into ions. The sulphuric acid remains in the electrolyte throughout the process and only the water is decomposed, producing two volumes of hydrogen for every one volume of oxygen. The electrons given up by the hydroxyl ions at the anode are propelled through the external circuit by the battery to the cathode where an equivalent number of electrons is taken up by the hydrogen ions. This constitutes the current in the external circuit. The movement of the ions to the oppositely charged electrodes V:42 ELECTROLYSIS OF COPPER SULPHATE SOLUTION If copper sulphate solution is used as the electrolyte and carbon rods as the anode and
cathode, copper will be deposited at the cathode soon after the voltage is applied (Chap. 31, Exp. 26). the copper sulphate is highly dissociated into positive copper ions (Cu^^) and negative sulphate ions (SO4--). In solution Cu SO 4 Cu"" + SO 4 - - The water is slightly dissociated into positive hydrogen ions (H"^) and negative hydroxyl ions (OH“). H 2O + OHis applied to When the voltage electrodes the following reactions occur: the At the Cathode 1. The copper ions and the hydrogen ions are attracted. 2. The copper ions are discharged in preference to the hydrogen ions. Each copper ion takes two electrons from the cathode and becomes a neutral copper atom. Cu"" + 2e ^ Cu° 3. The copper atoms are deposited on the carbon rod. At the Anode 1. The sulphate ions and the hydroxyl ions are attracted. 2. The reactions are exactly the same as in the electrolysis of water (Sec. V:42), in which oxygen bubbles were formed. Commercial use has been made of such a process in the electroplating industry (Sec. V:45), in which copper is used as the anode and the object to be plated as the cathode. Also, in the purification of various metals, a bar of impure metal 297 Chap. 26 MAGNETISM AND ELECTRICITY is used as the anode, pure metal as the cathode and a solution of a salt of the same metal as the electrolyte. Only the pure metal is transferred from the anode to the cathode where bars of pure metal are obtained. The impurities are left in the electrolytic cell. V:43 LAWS OF ELECTROLYSIS From your experimental work on electrolysis it will be apparent that there is a close connection between the current strength used and the amount of material that is decomposed (Chap. 31, Exp. It will also be readily noted in 27). the previous examples that the greater the time that the current flows, the greater the amounts of water decomposed or copper deposited. Further, it is not difficult to show that a greater mass of silver than of copper will be deposited using the same current for the same length of time. These observations were made as long ago as 1834 by Faraday who formulated Faraday’s Laws of Electrolysis as follows: 1. The amount of chemical change produced (i.e
., the amount of any sub- 298 stance deposited) by an electric current is proportional to the quantity of electricity passed (Quantity = Current X Time.) 2. The amounts of different substances deposited by the same quantity of electricity are proportional to their equiva(The equivalent weight lent weights. of a substance is the weight of the substance deposited by 96,400 coulombs.) The number of grams of various elements liberated by one ampere in one electrochemical second equivalent of the element. called the is Electrochemical Equivalents Aluminum Chlorine Copper Hydrogen Magnesium Oxygen Potassium Silver Sodium Zinc 0.000093 0.000368 0.000329 0.0000105 0.000126 0.0000829 0.000405 0.001118 0.000238 0.000339 V ;44 THE COPPER VOLTAMETER The internationally accepted definition of the ampere is based on the deposition of metal at the cathode of an electrolytic cell or voltameter. Silver was selected as the standard, since the relatively large amount of silver deposited in a short time enables a greater degree of accuracy in weighing, and because silver is very resistant to oxidation. The international ampere is defined as that current which, when passed through a solution of silver nitrate in accordance with given specifiat the rate of cations, 0.001118 gm. per second. deposits silver While silver is the best substance for accurate results, a copper voltameter is current satisfactory strength in elementary work (Chap. 31, Exp. 28). In this experiment both anode determining for CHEMICAL EFFECTS OF ELECTRIC CURRENT Sec. V:45 and cathode should be copper and the electrolyte copper sulphate solution. The circuit is adjusted so that a small current flows. The cathode should be thoroughly cleaned with fine emery paper, washed and dried. It is then carefully weighed. Next the is connected, as circuit in Fig. 26:3, and the current is allowed to flow for exactly twenty minutes. The cathode is removed, dipped in alcohol or ether and allowed to dry by evaporaIt is then carefully reweighed. The this tion. current may be calculated as example. in Example Initial weisfht of cathode = 5.52 gm. = 5.71 gm. =0.19 gm. = 20 min. = 1200 sec..‘. Weight of copper deposited Time of current flow Electro
chemical equivalent of copper = 0.000329 In 1200 sec. weight of copper deposited =0.19 gm..'. In 1 sec. weight of copper deposited = 0.19 = 0.000158 srm. Current flowing when 0.000329 gm. copper is deposited in 1 sec. = 1 amp. Current flowing when 1 gm. copper is deposited in 1 sec. = amp. 000329 1200 Current flowing when.000158 gm. copper is deposited in 1 sec. = 0.000158 X = 0.48 amp. 0.000329.'. The current strength is 0.48 amp. V:45 ELECTROPLATING Electroplating is an important industrial process designed to improve the appearance, or resistance increase to corrosion, of various metals. It consists of covering the metal with a thin layer silver, chromium, copper, etc., by of electrolysis. The article to be plated serves as the cathode and a solution of a compound of the metal to be deposited makes up the electrolyte (Chap. 31, Exp. 29). Before plating, the object must be thoroughly cleaned of rust, grease, etc. This is usually accomplished by treatment with abrasives followed by rinsing in strong acid, then strong alkali, then weak acid again, and finally distilled In order to obtain a fine longwater. lasting deposit a small current over a long time interval must be used. Special platings require modifications in the process. For example, silver plating is usually preceded by copper plating to give a suitable base. In copper plating better results are obtained if a little sulphuric acid is added to the electrolyte. Chromium plating directly on another metal leaves small openings like pin-holes in the surface so that corrosion may begin below the chromium layer. To avoid this the base metal is often lightly coated with nickel before the chromium is applied. Electroplating has also been applied to the printing industry in the reproduction of pages of type and illustrations, a process called electrotyping. An impression of the original is made in wax or plastic. This mould is covered with graphite or metallic powder to serve as a conductor 299 Chap. 26 MAGNETISM AND ELECTRICITY Industrial Electroplating. By Electrolysis These Metal Plates are Being Coated with a Thin Layer of Copper. International Nickel Co. of Canada and is then used as the cathode in a copper or nickel electrolytic cell. The metal deposited on
it is stripped off, backed with a metal of low melting-point to strengthen it and is then ready for use. This reproduction can be used over and over again and is readily stored for later editions. V:46 THE LEAD-ACID STORAGE BATTERY When the simple voltaic cell (Sec. V;23), and the dry cell (Sec. V:25), become discharged they must be discarded and replaced by new cells. Cells of this type are classified as primary cells. The lead storage cell differs from these in that once its chemical energy 300 has been exhausted, the cell may be restored to its original condition by electrical means. called secondary cells. The familiar lead-acid storage battery used in the electrical system of many automobiles consists of six secondary cells connected in series Such cells are 12 volts. provide approximately to Chemical energy is stored in the active materials of the plates and in the electrolyte when current is passed through during charging. This chemical energy is transformed into electrical energy as the cells are discharged in providing current in a circuit (Chap. 31, Exp. 30). (a) Structure of a Cell Several positive plates, consisting of CHEMICAL EFFECTS OF ELECTRIC CURRENT Sec. V : 46 VENT PLUGS SEALED COVER ELEMENT PROTECTOR SEPARATOR NEGATIVE PLATE PLATE HARD RUBBER CONTAINER SEDIMENT SPACE Exide Automotive Division Fig. 26:4 Structure of a Lead-Acid Storage Battery. lead peroxide forced into a strong grid of lead alloy, are joined to each other by metal strips (Fig. 26:4). Between each of these, and at the ends, are negative electrodes of spongy lead. These are connected by metal strips and kept plates by from touching the positive wood separators. The plates are contained in a moulded, hard rubber case holding the dilute sulphuric acid which serves as the electrolyte. (b) Discharging the Cell As the cell is used to provide the E.M.F. which causes current to flow in a circuit, it becomes discharged. The sulphuric acid combines with the porous materials of the plates and the following chemical reaction occurs: negative positive diluted plates electrolyte lead + lead peroxide + sulphuric acid -» lead sulphate + water both plates plates electrolyte As the two plates become coated with the same material the potential difference decreases. Simultaneously, the removal of sulphuric acid from the electrolyte and
the formation of water causes dilution of the acid in the cell. Thus, discharged cells are indicated by a lowering of the P.D. of the cell and a decrease in the specific gravity of the electrolyte. A fully charged cell should have a P.D. of approximately 2.2 volts, and 301 Chap. 26 MAGNETISM AND ELECTRICITY a specific gravity of 1.275 to 1.300. specific gravity falls to 1.185. (c) Recharging the Cell It is ready for recharging when the In order to recharge the cell direct current from a rectifier or some other source must be passed through the cell in the direction opposite to that of discharge. The chemical reactions in the cells are reversed: diluted negative both plates lead sulphate + water electrolyte positive plates plates —» lead peroxide + lead + sulphuric acid electrolyte Thus, the plates are again made dissimilar and the P.D. increases to 2.2 volts. At the same time water is used up and sulphuric acid is produced by the reaction, so the specific gravity of the electrolyte increases. The charging and discharging reactions may be summarized as: negative positive electrolyte both plates diluted plates plates lead + lead peroxide + s (d) Care of Storage Batteries 1. Keep the battery clean and dry. 2. Do not allow the battery to dis- 3. Keep the charge below specific gravity 1.185. above the level of the wood separators by addition of distilled water. electrolyte 4. Do not allow a fully discharged cell to stand in this condition for more than a few days before charging. (e) Battery Rating The life of a battery is rated in ampere-hours, i.e., amperes X hours. For example, a battery rated at 100 ampere-hours would be capable of de- discharge iric acid ^ lead sulphate + water electrolyte charge livering 5 amperes for 20 hours, or 12.5 amperes for 8 hours, etc. In general, the greater the number of plates per cell, the greater the ampere-hour capacity of the 3. battery. (f) Uses of Storage Batteries Storage cells are frequently used to provide a source of E.M.F. for extended periods of time, as in some radio transmitters and receivers. They are used in the starting circuits of automobiles and aircraft, for auxiliary power supplies for telephones, trains, submarines and ships and
for emergency lighting-systems. V : 47 Q U E S noNS A 1. (a) Define: ion, electrolyte, non-elec- trolyte, electrolytic cell, anode, cath- ode, anion, cation, electrolysis. (b) Outline Arrhenius’ theory of ion- ization. 2. Explain how the electrolyte completes In the electrolysis of water describe: (a) the condition of the water and the sulphuric acid before the voltage is applied. (b) what happens in the electrolyte at the moment when the voltage is the circuit in electrolysis. applied. 302 CHEMICAL EFFECTS OF ELECTRIC CURRENT Sec. V:47 (c) the reactions that occur at (i) the cathode (ii) the anode. lysis of water by a current of 2.0 amperes flowing for 4 hours? 4. Explain the electrolysis of copper 4. What current would deposit 0.1 sulphate solution. gm. of silver in 8 hours? 5. Describe how electrolysis may be used in (a) silver plating (b) refining of copper 5. A constant current is passed through 20 copper voltameter a minutes and it is found that 0.500 gm. of copper is deposited on the cathode. exactly for 6. 7. (c) electrotyping. (a) State Faraday’s Laws of Electro- lysis. (b) Define electrochemical equiva- lent. (a) Define an ampere in terms of the deposition of metal at the cathode of an electrolytic cell or voltameter. (b) Why Is acceptable Ohm’s Law? (c) Why was silver selected as the international standard rather than more on definition based than that this copper? (a) Describe the construction of a 8. lead-acid storage cell. (b) What transformations of energy (i) charging, (il) distake place in charging a lead-acid cell? (c) Give word equations describing the reactions as a lead-acid cell is 9. (i) charged, (Ii) discharged. (d) How may the condition of charge of such a storage battery be determined? (a) Define ampere-hour. (b) What determines the amperehour capacity of a battery? (c) What precautions should be
obstorage served caring for a in battery? B Calculate the strength of the current. 6. An ammeter connected in series with a silver voltameter reads 1.50 amperes. In 50 minutes the increase in weight of the cathode is 4.947 gm. What Is the error in the ammeter reading? 7. A copper voltameter and a water voltameter are connected in series with a direct current supply. In 25 minutes 0.09 gm. of copper is deposited on the cathode of the copper voltameter.. (a) What current is flowing in the circuit? (b) What mass of hydrogen is liberated in the water voltameter? 8. A current of 2 amperes is passed through a copper voltameter. Copper is deposited evenly on the cathode which has an area of 66 sq. cm. Find the thickness of the layer when the current has been flowing for 30 minutes. (Density of copper = 9.0 gm. per c.c.) 9. The anode of a copper voltameter is made of impure copper, and the particles of impurity detach themselves and fall to as cell bottom of the the electrolysis continues. A current of 2.0 amperes flows for 1 hour and 40 minutes. At the start the anode weighs 85.69 gm. and at the end 81.37 gm. Find the mass of copper dissolved from the anode and the mass of impurity released. 10 1. What weight of (a) copper (b) silver will be deposited in 3 hours by a current of 1 ampere? 2. What weight of (a) copper (b) silver will be deposited in 4 hours by a current of 2.0 amperes? 3. What weight of (a) oxygen (b) hydrogen would be liberated in the electro- series connected (a) If four 2 volt lead-acid cells, each of 0.1 ohm internal resistance, a are in conductor of 3.6 ohms resistance, what current would flow? (b) How long continue to flow if the battery has a capacity of 30 ampere-hours? would current with this 303 CHAPTER 27 MAGNETIC EFFECTS OF ELECTRIC CURRENT through a piece of cardboard, as shown in Fig. 27:1. When the switch is closed and iron filings are sprinkled lightly over the cardboard, gentle tapping will cause the filings to arrange themselves in
concentric circles with the wire as centre. Thus the pattern of the lines of magnetic force becomes apparent. The direction of these lines of force may be determined Left Hand Rule to DeterFig. 27:2 mine the Direction of the Magnetic Field about a Conductor. by placing a number of small magnetic compasses on the cardboard. The N-poles of the compasses indicate that the lines go in a counter-clockwise direction about the wire (Chap. 31, Exp. 31). It is apparent, then, that if the direction of current is known, the direction of the lines of force about a conductor may be determined as follows: Grasp the conductor with the left hand with the thumb extended in the direction of the electron flow ( — to + ). The fingers V:48 ELECTROMAGNETIC EFFECT In 1820, Hans Christian Oersted, professor of Physics at the University of Copenhagen, made a discovery that has made possible most of the modern advancements in electrical knowledge. He observed that a wire carrying an electric current deflected a compass-needle. Further that whenever a current was passing through a conductor a magnetic field was set up around it. experiments established It is possible to investigate this magconductor passing field by a netic Fig. 27:1 Magnetic Field about a Conductor. 304 MAGNETIC EFFECTS OF ELECTRIC CURRENT Sec. V:49 When considering the magnetic field about a helix, it is convenient to represent it as in Fig. 27:5. The helix is shown in cross-section with the front half removed. The electron flow is up the back section of the turns and down the front. In the diagram, electron flow is indicated by a dot (.) representing the head of an arrow and a cross ( + ) representing the Fig. 27:6a shows the lines of magtail. netic force around a few turns of wire. The Left-Hand Rule will confirm the will now point in the direction in which the lines of magnetic force encircle the is This called statement the wire. Left-Hand Rule (Fig. 27:2). Conversely, this rule may be used to determine the direction of the electron flow if the direction of the lines of force is known. V : 49 MAGNETIC FIELD ABOUT A HELIX A single turn of wire (Fig. 27:3) is called a loop or coil. A series of such Fig. 27:3 Magnetic Field about a Loop Carrying Electric Current. loops in
a wire (Fig. 27:4) is referred to as a helix or solenoid. If a conductor is formed into a single loop, the lines of Fig. 27:4 A Helix or Solenoid. magnetic force which surround the wire will pass through the centre of the loop as shown. Note that the magnetic field inside the loop will be more dense than outside since the lines of force are crowded into a smaller area. The Lines of Magnetic Force Fig. 27:6 Around the Individual Turns of Wire in a Helix as Shown at (a). Combine to Form the Resultant Field Shown at (b). Fig. 27:5 Cross-sectional View of a Helix with the Front Half Removed. The Direction of Electron Flow is Indicated. direction of these lines. Between the turns the forces are in opposite directions and so tend to cancel each other out. In the centre of the coils the forces act in the same direction and are very concentrated. On the outside of the helix the forces also reinforce each other to give us Fig. 27:6b. Note the similarity between this field represented in the 305 Chap. 27 MAGNETISM AND ELECTRICITY pattern and that formed by a bar magnet (Sec. V:4). The existence of field may be readily proved by inserting a helix, carrying current, in a slit in a piece of cardboard Iron filings 27:7). (Fig. will this Apparatus Used to DemonFig. 27:7 strate the Field of Force about a Helix Carrying Electric Current. the pattern of the magnetic indicate field (Chap. 31, Exp. 32). The polarity of the field may be determined by testing with a compass-needle. From this information a simple rule may be confirmed: Grasp the helix in the left hand so that the fingers extend in the direction the electrons are flowing around the turns. The extended thumb will then point towards the N-pole of the helix This may be called the (Fig. 27:8). Left-Hand Rule for the Helix or, to avoid confusion with other rules, simply the Helix Rule. V:50 ELECTROMAGNETS If a bar of iron is placed in the centre of a coil of wire through which a cur- 306 rent is flowing, the iron will become magnetized. The elementary magnets of the iron become aligned in such a direction as to reinforce the magnetic field of the coil. Thus the iron core greatly strengthens the magnetic field
. Such an arrangement is known as an electromagnet. Soft iron makes the most satisfactory core, since a temporary magnet is produced. When the current in the is stopped the magnetism of the coil core is lost in a short time. An increase in the number of turns in the coil or an increase in the strength of the electric current flowing through it will result in a more powerful electromagnet (Chap. 31, Exp. 33). Electromagnets have been designed in a variety of shapes to meet many needs. The iron clad type is widely used where strong magnetic fields are desirable as Iron Core * ^ 1 \ Electron Flow 1 ) ) ) ) ) )..--1 1 I. ^ ^ 2 r 1 Fig. 27:9 Iron-Clad Electromagnet. for a lifting magnet for scrap iron or in radio loudspeakers. The iron core not only passes through the centre, but almost completely surrounds it as shown in Fig. 27:9. The horseshoe electromagnet (Fig. 27:10) is used in such devices as earphones, telephone receivers, electric bells and electric buzzers. The electric bell (Fig. 27:11) consists of a gong, a horseshoe electromagnet, soft iron armature and contact screw arranged in a circuit as shown. When the switch is closed MAGNETIC EFFECTS OF ELECTRIC CURRENT Sec. V:50 loses The electromagnet broken. its magnetism and the armature is pulled back to the contact point by the spring. This completes the circuit and the action Thus, the hammer will is vibrate against the gong as long as the switch is depressed and a continuous ringing is produced. repeated. Electromagnets are being used more and more to protect circuits carrying large currents. Magnetic circuit breakers employ a switch which is opened by the magnet if current becomes too strong. A simple circuit is shown in Fig. 27:12. The student should trace the the Fig. 27:10 The Horseshoe Electromagnet. current flows in the winding ot the electromagnet, causing the armature to be attracted. As the armature moves away from the contact screw the circuit is Magnetic Circuit Breaker. Fig. 27:12 If current becomes too great, core is pulled upwards by magnetism of the coil, tripping the catch held by Si. pulls up the knife switch Spring S 2 breaking the circuit. path of the electrons and explain the action of the circuit breaker
. The automobile generator cut-out relay is a magnetic switch which opens and closes the circuit between the genbattery erator (Sec. V:63) and the 307 Chap. 27 MAGNETISM AND ELECTRICITY An Electromagnet Used for Lifting Scrap Iron. steel Co. of Canada Ltd. (Sec. V:46). It serves to connect the generator to the battery when the generator is operating at charging speeds and to open the circuit when the generator stops or slows down to prevent back the through the generator. A simple circuit is shown in Fig. 27 : 13. discharging battery from The cut-out relay has two windings assembled on the same soft iron core. The shunt winding (dotted) is connected in parallel with the generator so that, when the generator starts to operate, the potential difference created causes a current to flow through the winding. This 308 produces a magnetic field strong enough to pull the armature toward the core, and the circuit is closed as the contact points meet. Current then flows from the and back generator through “ground”, passing through the series winding in such a direction as to add armature down. the magnetism holding battery the the to to When the generator slows down, the voltage produced by the generator becomes less than the voltage. Thus, a current begins to flow in the reverse direction through the series winding but continues to flow in the same battery MAGNETIC EFFECTS OF ELECTRIC CURRENT Sec. V:52 the shunt winding. The direction in magnetic fields of the two windings are now in opposite directions and so tend to cancel each other. The armature is pulled upward by spring tension to open Fig. 27:14 A Simple Galvanoscope. parison of current strengths may be made. For weak currents the coils with many turns will be used and for strong currents the coils with few turns are satisfactory (Sec. V:50). This instrument has been largely replaced by more sensitive and more accurate current-measuring devices. Fig. 27:13 Automobile Generator Cut-Out Relay. V:52 THE MOTOR PRINCIPLE the contact points and the broken between the is battery and the circuit generator. V;51 THE GALVANOSCOPE The galvanoscope is a simple device used to determine the directions and comparative strengths of electric curIt consists of several coils having rents. varying numbers of turns of wire (Fig. 27:14). The current is made to pass over a compass-need

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