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vertex : point where the mirrorâs surface intersects with the optical axis | https://openstax.org/books/university-physics-volume-3/pages/2-key-terms |
virtual image : image that cannot be projected on a screen because the rays do not physically go through the image, they only appear to originate from the image | https://openstax.org/books/university-physics-volume-3/pages/2-key-terms |
A plane mirror always forms a virtual image (behind the mirror). | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The image and object are the same distance from a flat mirror, the image size is the same as the object size, and the image is upright. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Spherical mirrors may be concave (converging) or convex (diverging). | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The focal length of a spherical mirror is one-half of its radius of curvature:f=R/2f=R/2. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The mirror equation and ray tracing allow you to give a complete description of an image formed by a spherical mirror. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Spherical aberration occurs for spherical mirrors but not parabolic mirrors; comatic aberration occurs for both types of mirrors. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
This section explains how a single refracting interface forms images. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
When an object is observed through a plane interface between two media, then it appears at an apparent distancehihithat differs from the actual distancehoho:hi=(n2/n1)hohi=(n2/n1)ho. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
An image is formed by the refraction of light at a spherical interface between two media of indices of refractionn1n1andn2n2. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Image distance depends on the radius of curvature of the interface, location of the object, and the indices of refraction of the media. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Two types of lenses are possible: converging and diverging. A lens that causes light rays to bend toward (away from) its optical axis is a converging (diverging) lens. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
For a converging lens, the focal point is where the converging light rays cross; for a diverging lens, the focal point is the point from which the diverging light rays appear to originate. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The distance from the center of a thin lens to its focal point is called the focal lengthf. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Ray tracing is a geometric technique to determine the paths taken by light rays through thin lenses. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
A real image can be projected onto a screen. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
A virtual image cannot be projected onto a screen. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
A converging lens forms either real or virtual images, depending on the object location; a diverging lens forms only virtual images. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Image formation by the eye is adequately described by the thin-lens equation. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The eye produces a real image on the retina by adjusting its focal length in a process called accommodation. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Nearsightedness, or myopia, is the inability to see far objects and is corrected with a diverging lens to reduce the optical power of the eye. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Farsightedness, or hyperopia, is the inability to see near objects and is corrected with a converging lens to increase the optical power of the eye. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
In myopia and hyperopia, the corrective lenses produce images at distances that fall between the personâs near and far points so that images can be seen clearly. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Cameras use combinations of lenses to create an image for recording. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Digital photography is based on charge-coupled devices (CCDs) that break an image into tiny âpixelsâ that can be converted into electronic signals. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
A simple magnifier is a converging lens and produces a magnified virtual image of an object located within the focal length of the lens. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Angular magnification accounts for magnification of an image created by a magnifier. It is equal to the ratio of the angle subtended by the image to that subtended by the object when the object is observed by the unaided eye. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Angular magnification is greater for magnifying lenses with smaller focal lengths. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Simple magnifiers can produce as great as tenfold (10Ã10Ã) magnification. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Many optical devices contain more than a single lens or mirror. These are analyzed by considering each element sequentially. The image formed by the first is the object for the second, and so on. The same ray-tracing and thin-lens techniques developed in the previous sections apply to each lens element. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The overall magnification of a multiple-element system is the product of the linear magnifications of its individual elements times the angular magnification of the eyepiece. For a two-element system with an objective and an eyepiece, this isM=mobjMeye.M=mobjMeye.2.41wheremobjmobjis the linear magnification of the obje... | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The microscope is a multiple-element system that contains more than a single lens or mirror. It allows us to see detail that we could not to see with the unaided eye. Both the eyepiece and objective contribute to the magnification. The magnification of a compound microscope with the image at infinity isMnet=â(16cm)(2... | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Simple telescopes can be made with two lenses. They are used for viewing objects at large distances. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
The angular magnificationMfor a telescope is given byM=âfobjfeye,M=âfobjfeye,2.43wherefobjfobjandfeyefeyeare the focal lengths of the objective lens and the eyepiece, respectively. | https://openstax.org/books/university-physics-volume-3/pages/2-summary |
Πl = m λ , Πl = m λ , for m = 0, ±1, ±2, ±3⦠| https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
Πl = ( m + 1 2 ) λ , Πl = ( m + 1 2 ) λ , for m = 0, ±1, ±2, ±3⦠| https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
Πl = d sin θ Πl = d sin θ | https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
d sin θ = m λ , for m = 0 , ± 1 , ± 2 , ± 3 ,⦠d sin θ = m λ , for m = 0 , ± 1 , ± 2 , ± 3 ,⦠| https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
d sin θ = ( m + 1 2 ) λ , for m = 0, ± 1 , ± 2 , ± 3 , ⦠d sin θ = ( m + 1 2 ) λ , for m = 0, ± 1 , ± 2 , ± 3 , ⦠| https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
y m = m λ D d y m = m λ D d | https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
Πd = m λ 0 2 Πd = m λ 0 2 | https://openstax.org/books/university-physics-volume-3/pages/3-key-equations |
coherent waves : waves are in phase or have a definite phase relationship | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
fringes : bright and dark patterns of interference | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
incoherent : waves have random phase relationships | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
interferometer : instrument that uses interference of waves to make measurements | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
monochromatic : light composed of one wavelength only | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
Newtonâs rings : circular interference pattern created by interference between the light reflected off two surfaces as a result of a slight gap between them | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
order : integermused in the equations for constructive and destructive interference for a double slit | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
principal maximum : brightest interference fringes seen with multiple slits | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
secondary maximum : bright interference fringes of intensity lower than the principal maxima | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
thin-film interference : interference between light reflected from different surfaces of a thin film | https://openstax.org/books/university-physics-volume-3/pages/3-key-terms |
Youngâs double-slit experiment gave definitive proof of the wave character of light. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
An interference pattern is obtained by the superposition of light from two slits. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
In double-slit diffraction, constructive interference occurs whendsinθ=mλ(form=0,±1,±2,±3â¦)dsinθ=mλ(form=0,±1,±2,±3â¦), wheredis the distance between the slits,θθis the angle relative to the incident direction, andmis the order of the interference. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
Destructive interference occurs whendsinθ=(m+12)λform=0,±1,±2,±3,â¦dsinθ=(m+12)λform=0,±1,±2,±3,â¦. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
Interference from multiple slits (N>2N>2) produces principal as well as secondary maxima. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
As the number of slits is increased, the intensity of the principal maxima increases and the width decreases. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
When light reflects from a medium having an index of refraction greater than that of the medium in which it is traveling, a180°180°phase change (or aλ/2λ/2shift) occurs. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
Thin-film interference occurs between the light reflected from the top and bottom surfaces of a film. In addition to the path length difference, there can be a phase change. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
When the mirror in one arm of the interferometer moves a distance ofλ/2λ/2each fringe in the interference pattern moves to the position previously occupied by the adjacent fringe. | https://openstax.org/books/university-physics-volume-3/pages/3-summary |
a sin θ = m λ for m = ± 1 , ± 2 , ± 3 , .. . a sin θ = m λ for m = ± 1 , ± 2 , ± 3 , .. . | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
β = Ï 2 = Ï a sin θ λ β = Ï 2 = Ï a sin θ λ | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
E = N ΠE 0 sin β β E = N ΠE 0 sin β β | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
I = I 0 ( sin β β ) 2 I = I 0 ( sin β β ) 2 | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
θ = 1.22 λ D θ = 1.22 λ D | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
m λ = 2 d sin θ , m = 1 , 2 , 3 .. . m λ = 2 d sin θ , m = 1 , 2 , 3 .. . | https://openstax.org/books/university-physics-volume-3/pages/4-key-equations |
Bragg planes : families of planes within crystals that can give rise to X-ray diffraction | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
destructive interference for a single slit : occurs when the width of the slit is comparable to the wavelength of light illuminating it | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
diffraction : bending of a wave around the edges of an opening or an obstacle | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
diffraction grating : large number of evenly spaced parallel slits | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
diffraction limit : fundamental limit to resolution due to diffraction | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
hologram : three-dimensional image recorded on film by lasers; the word hologram meansentire picture(from the Greek wordholo, as in holistic) | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
holography : process of producing holograms with the use of lasers | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
missing order : interference maximum that is not seen because it coincides with a diffraction minimum | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
Rayleigh criterion : two images are just-resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
resolution : ability, or limit thereof, to distinguish small details in images | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
two-slit diffraction pattern : diffraction pattern of two slits of widthDthat are separated by a distancedis the interference pattern of two point sources separated bydmultiplied by the diffraction pattern of a slit of widthD | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
width of the central peak : angle between the minimum form=1m=1andm=â1m=â1 | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
X-ray diffraction : technique that provides the detailed information about crystallographic structure of natural and manufactured materials | https://openstax.org/books/university-physics-volume-3/pages/4-key-terms |
Diffraction can send a wave around the edges of an opening or other obstacle. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
A single slit produces an interference pattern characterized by a broad central maximum with narrower and dimmer maxima to the sides. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
The intensity pattern for diffraction due to a single slit can be calculated using phasors asI=I0(sinββ)2,I=I0(sinββ)2,whereβ=Ï2=Ïasinθλβ=Ï2=Ïasinθλ,ais the slit width,λλis the wavelength, andθθis the angle from the central peak. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
With real slits with finite widths, the effects of interference and diffraction operate simultaneously to form a complicated intensity pattern. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Relative intensities of interference fringes within a diffraction pattern can be determined. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Missing orders occur when an interference maximum and a diffraction minimum are located together. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
A diffraction grating consists of a large number of evenly spaced parallel slits that produce an interference pattern similar to but sharper than that of a double slit. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Constructive interference occurs whendsinθ=mλform=0,±1,±2,...,dsinθ=mλform=0,±1,±2,...,wheredis the distance between the slits,θθis the angle relative to the incident direction, andmis the order of the interference. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Diffraction limits resolution. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
The Rayleigh criterion states that two images are just resolvable when the center of the diffraction pattern of one is directly over the first minimum of the diffraction pattern of the other. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
X-rays are relatively short-wavelength EM radiation and can exhibit wave characteristics such as interference when interacting with correspondingly small objects. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Holography is a technique based on wave interference to record and form three-dimensional images. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Lasers offer a practical way to produce sharp holographic images because of their monochromatic and coherent light for pronounced interference patterns. | https://openstax.org/books/university-physics-volume-3/pages/4-summary |
Î t = Î Ï 1 â v 2 c 2 = γ Ï Î t = Î Ï 1 â v 2 c 2 = γ Ï | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
γ = 1 1 â v 2 c 2 γ = 1 1 â v 2 c 2 | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
L = L 0 1 â v 2 c 2 = L 0 γ L = L 0 1 â v 2 c 2 = L 0 γ | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
x = x â² + v t , y = y â² , z = z â² , t = t â² x = x â² + v t , y = y â² , z = z â² , t = t â² | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
t = t â² + v x â² / c 2 1 â v 2 / c 2 t = t â² + v x â² / c 2 1 â v 2 / c 2 | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
x = x â² + v t â² 1 â v 2 / c 2 x = x â² + v t â² 1 â v 2 / c 2 | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
y = y â² y = y â² | https://openstax.org/books/university-physics-volume-3/pages/5-key-equations |
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