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show up with unpolarized light. But as we see from the defnition, light is
unpolarized only if we are unable ©o fñnd out whether the light is polarized or
33-2 Polarization of scattered light
The first example of the polarization efect that we have already discussed
1s the scattering of lipht. Consider a beam of light, for example from the sun,
shining on the air. The electric feld will produce oscillations of charges in the
air, and motion of these charges will radiate light with its maximum intensity
in a plane normal to the direction of vibration of the charges. The beam from
the sun is unpolarized, so the direction of polarization changes constantly, and
the direction of vibration of the charges in the air changes constantly. lÝ we
consider light scattered at 90, the vibration of the charged particles radiates
to the observer only when the vibration is perpendicular to the observerˆs line
of sight, and then light will be polarized along the direction of vibration. So
scattering is an example of one means of producing polarization.
33-3 Birefringence
Another interesting efect of polarization is the fact that there are substances
for which the index of refraction is diferent for light linearly polarized in one
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direction and linearly polarized in another. Suppose that we had some material
which consisted of long, nonspherical molecules, longer than they are wide, and
suppose that these molecules were arranged in the substance with their long axes
parallel. Then what happens when the oscillating electric ñeld passes through this
substance? Suppose that because of the structure of the molecule, the electrons
in the substanece respond more easily to oscillations in the direction parallel to
the axes of the molecules than they would respond I1 the electric ñeld tries to
push them at right angles to the molecular axis. In this way we expect a diferent
response for polarization in one direction than for polarization at right angles to
that direction. Let us call the direction of the axes of the molecules the opfic #3.
'When the polarization is in the direction of the optic axis the index of refraction
is diÑerent than it would be if the direction of polarization were at right angles
to it. Such a substance is called b#eƒringenmt. It has two refrangibilities, i.e.,
two indexes of refraction, depending on the direction of the polarization inside
the substance. What kind of a substance can be birefingent? In a birefringent
substance there must be a certain amount of lining up, for one reason or another,
of unsymmetrical molecules. Certainly a cubic crystal, which has the symmetry of
a cube, cannot be birefringent. But long needlelike crystals undoubtedly contain
mmolecules that are asymmetric, and one observes this effect very easily.
Let us see what efects we would expect if we were to shine polarized light
through a plate of a birefringent substance. lf the polarization is parallel to
the optic axis, the light will go through with one velocity; 1f the polarization is
perpendicular to the axis, the light is transmitted with a diferent velocity. An
Interesting situation arises when, say, light is linearly polarized at 45° to the
optic axis. NÑow the 45° polarization, we have already noticed, can be represented
as a superposition of the z- and the ¿-polarizations of equal amplitude and in
phase, as shown in EFig. 33-2(a). Since the z- and z-polarizations travel with
diferent velocities, their phases change at a diferent rate as the light passes
through the substance. So, although at the start the z- and ø-vibrations are in
phase, inside the material the phase diference between z- and ø-vibrations 1s
proportional to the depth in the substance. As the light proceeds through the
material the polarization changes as shown in the series oŸ diagrams in Fig. 33-2.
Tf the thickness of the plate is just right to introduce a 90° phase shift between
the z- and g-polarizations, as in Fig. 33-2(c), the light will come out circularly
polarized. Such a thickness is called a quarter-wave plate, because it introduces a
quarter-cycle phase diference between the zø- and the -polarizations. If linearly
polarized light is sent through ©wo quarter-wave plates, it will come out plane-
--- Trang 574 ---
polarized again, but at right angles to the original direction, as we can see from
Eig. 33-2(e).
One can easily illustrate this phenomenon with a piece of cellophane. Cello-
phane is made of long, fbrous molecules, and is not isotropic, since the fibers
lie preferentially in a certain direction. 'To demonstrate birefringence we need a
beam of linearly polarized light, and we can obtain this conveniently by passing
unpolarized light through a sheet of polaroid. Polaroid, which we will discuss
later in more detail, has the useful property that it transmits light that is linearly
polarized parallel to the axis of the polaroid with very little absorption, but
light polarized in a direction perpendicular to the axis of the polaroid is strongly
absorbed. When we pass unpolarized light through a sheet of polaroid, only that
part of the unpolarized beam which is vibrating parallel to the axis of the polaroid
gets through, so that the transmitted beam is linearly polarized. 'This same
property of polaroid is also useful in detecting the direction of polarization of a
linearly polarized beam, or in determining whether a beam is linearly polarized or
not. Ône simply passes the beam of light through the polaroid sheet and rotates
the polaroid in the plane normal to the beam. lf the beam 1s linearly polarized,
it will not be transmitted through the sheet when the axis of the polaroid is
normal to the direction of polarization. The transmitted beam is only slightly
attenuated when the axis of the polaroid sheet is rotated through 90”. Tf the
transmitted intensity is independent of the orientation of the polaroid, the beam
is not linearly polarized.
To demonstrate the birefringence of cellophane, we use two sheets of polaroid,
as shown in Eig. 33-3. The frst gives us a linearly polarized beam which we pass
through the cellophane and then through the second polaroid sheet, which serves
to detect any efect the cellophane may have had on the polarized light passing
CELLOPHANE
+1 :HÉ“
XS stasopf
Fig. 33-3. An experimental demonstration of the birefringence of
cellophane. The electric vectors ¡n the light are indicated by the dot-
ted lines. The pass axes of the polaroid sheets and optic axes of the
cellophane are indicated by arrows. 'The incident beam is unpolarized.
--- Trang 575 ---
through it. If we first set the axes of the two polaroid sheets perpendicular to each
other and remove the cellophane, no light will be transmitted through the second
polaroid. If we now introduce the cellophane between the two polaroid sheets, and
rotate the sheet about the beam axis, we observe that in general the cellophane
makes it possible for some light to pass through the second polaroid. However,
there are two orientations of the cellophane sheet, at right angles to each other,
which permit no light to pass through the second polaroid. 'Phese orientations in
which linearly polarized light is transmitted through the cellophane with no efect
on the direction of polarization must be the directions parallel and perpendicular
to the optic axis of the cellophane sheet.