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we do not understand the fundamental mechanism yet, we will some day, and |
we can understand even now how the interference occurs. For example, when |
a light wave hits a surface of a material with an index ø, let us say at normal |
incidence, some of the light is refected. The reasơn for the reflection we are not |
in a position to understand right now; we shall discuss it later. But suppose we |
know that some of the light is refected both on entering and leaving a refracting |
medium. 'Phen, if we look at the refection of a light source in a thin film, we |
see the sum of two waves; If the thicknesses are small enoupgh, these two waves |
* 'This is because Rayleigh”s criterion is a rough idea in the frst place. It tells you where it |
begins to get very hard to tell whether the image was made by one or by two stars. Actually, if |
sufficiently careful measurements of the exact intensity distribution over the difracted image |
spot can be made, the fact that two sources make the spot can be proved even ïif Ø is less |
than À/L. |
--- Trang 525 --- |
will produce an interference, either constructive or destructive, depending on |
the signs of the phases. It might be, for instance, that for red light, we get an |
enhanced reflection, but for blue light, which has a diÑerent wavelength, perhaps |
we get a destructively interfering reflection, so that we see a bright red reflection. |
l we change the thickness, i.e., if we look at another place where the film 1s |
thicker, it may be reversed, the red interfering and the blue not, so it is bright |
blue, or green, or yellow, or whatnot. So we see colors when we look at thin flms |
and the colors change if we look at diferent angles, because we can appreciate |
that the timings are diferent at diferent angles. Thus we suddenly appreciate |
another hundred thousand situations involving the colors that we see on oil ñlms, |
soap bubbles, etc. at diferent angles. But the principle is all the same: we are |
only adding waves at diferent phases. |
As another important application of difraction, we may mention the following. |
W© used a grating and we saw the difracted image on the sereen. If we had used |
mmonochromatic light, it would have been at a certain specifc place. Then there |
were various higher-order images also. Erom the positions of the images, we could |
tell how far apart the lines on the grating were, if we knew the wavelength of |
the light. Erom the difference in intensity of the various images, we could ñnd |
out the shape of the grating scratches, whether the grating was made of wires, |
sawtooth notches, or whatever, t#thout being ablÌe to see them. This principle 1s |
used to discover the positions of the ø‡oms ?n a crustal. 'Phe only complication |
1s that a crystal is three-dimensional; it is a repeating three-dimensional array |
of atoms. We cannot use ordinary light, because we must use something whose |
wavelength is less than the space between the atoms or we get no effect; so we |
must use radiation of very short wavelength, i.e., x-rays. 5o, by shining x-rays |
into a crystal and by noticing how intense is the refection in the various orders, |
we can determine the arrangement of the atoms inside without ever being able |
to see them with the eyel It is in this way that we know the arrangement of the |
atoms in various substances, which permitted us to draw those pictures In the |
ñrst chapter, showing the arrangement of atoms in salt, and so on. We shaÏll later |
come back to this subject and discuss 1t in more detail, and therefore we say no |
more about this most remarkable idea at present. |
30-6 Diffraction by opaque screens |
Now we come to a very interesting situation. Suppose that we have an opaque |
sheet with holes in it, and a light on one side of it. We want to know what the |
--- Trang 526 --- |
Intensity Is on the other side. What most people say is that the light shines |
through the holes, and produces an efect on the other side. It will turn out that |
one gets the right answer, to an excellent approximation, if he assumes that there |
are sources distributed with uniform density across the open holes, and that |
the phases of these sources are the same as they would have been ïf the opaque |
material were absent. Of course, actually there are øoø sources at the holes, In |
fact that is the only place that there are certaznl no sources. Nevertheless, we |
get the correct difraction patterns by considering the holes to be the only places |
that there are sources; that 1s a rather peculiar fact. We shall explain later why |
this is true, but for now let us just suppose that it 1s. |
In the theory of difraction there is another kind of difraction that we should |
briefly discuss. It is usually not discussed in an elementary course as early as this, |
only because the mathematical formulas involved in adding these little vectors |
are a little elaborate. Otherwise i% is exactly the same as we have been doïng all |
along. AlI the interference phenomena are the same; there is nothing very much |
more advanced involved, only the cireumstances are more complicated and it is |
harder to add the vectors together, that is all. |
Suppose that we have light coming in from infnity, casting a shadow of an |
object. Pigure 30-7 shows a screen on which the shadow of an object 4? is made |
by a light source very far away compared with one wavelength. NÑow we would |
expect that outside the shadow, the intensity is all bright, and inside 1t, it 1s |
all dark. As a matter of fact, if we plot the intensity as a function of position |
— > E |
—> 'h s |
————*® |
— > A |
Opaque Screen |
Object |
Fig. 30-7. A distant light source casts a shadow of an opaque obJect |
on a screen. |
--- Trang 527 --- |
near the shadow edge, the intensity rises and then overshoots, and wobbles, and |
oscillates about in a very peculiar manner near this edge (Eig. 30-9). We now |
shall discuss the reason for this. If we use the theorem that we have not yet |
proved, then we can replace the actual problem by a set of efective sources |
uniformly distributed over the open space beyond the object. |
We imagine a large number of very closely spaced antennas, and we wan$ |
the intensity at some point P. That looks just like what we have been doïng. |
Not quite; because our screen is not at infnity. We do not want the intensity |
at infnity, but at a fñnite point. To calculate the intensity at some particular |
place, we have to add the contributions from all the antennas. Eirst there is an |
antenna at D, exactly opposite ; ïf we go up a little bít in angle, let us say a |
height h, then there is an increase in delay (there is also a change in amplitude |
because of the change in distance, but this is a very small efect if we are at all |
far away, and is much less important than the diference in the phases). NÑow the |
path diference PP — DP is approximately h2/2s, so that the phase diferenee is |
proportional to the sợuare of how far we go trom , while in our previous work |
øs was infinite, and the phase difference was zneariu proportional to h. When |
the phases are linearly proportional, each vector adds at a constant angle to the |
next vector. What we now need is a curve which is made by adding a lot of |
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