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W© suppose that the light passes through the cellophane with bwo diferent
velocities in these two diferent orientations, but it is transmitted without changing
the direction of polarization. When the cellophane is turned halfway bebween
these two orientations, as shown in Eig. 33-3, we see that the light transmitted
through the second polaroid is bright.
Tt just happens that ordinary cellophane used in commercial packaging is
very close to a halfwave thickness for most of the colors in white light. Such
a sheet will turn the axis of linearly polarized light through 90° if the incident
linearly polarized beam makes an angle of 45° with the optic axis, so that the
beam emerging from the cellophane is then vibrating in the right direction to
pass through the second polaroid sheet.
TÝ we use white light in our demonstration, the cellophane sheet will be of the
proper half-wave thickness only for a particular component of the white light,
and the transmitted beam will have the color of this component. “The color
transmitted depends on the thickness of the cellophane sheet, and we can vary
the efective thickness of the cellophane by tilting i% so that the light passes
throuph the cellophane at an angle, consequently through a longer path in the
cellophane. As the sheet is tilted the transmitted color changes. With cellophane
of diferent thicknesses one can construct filters that will transmit diferent colors.
These flters have the interesting property that they transmit one color when the
two polaroid sheets have their axes perpendicular, and the complementary color
when the axes of the bwo polaroid sheets are parallel.
Another interesting application of aligned molecules is quite practical. Certain
plastics are composed oŸ very long and complicated molecules all twisted together.
'When the plastic is solidified very carefully, the molecules are all twisted in a mass,
so that there are as many aligned in one direction as another, and so the plastic
is not particularly birefringent. Usually there are strains and stresses introduced
--- Trang 576 ---
when the material is solidifed, so the material is not perfectly homogeneous.
However, if we apply tension to a piece of this plastic material, it is as iÍ we were
pulling a whole tangle of strings, and there will be more strings preferentially
aligned parallel to the tension than in any other direction. So when a stress 1s
applied to certain plastics, they become birefringent, and one can see the efects
of the birefringence by passing polarized light through the plastic. If we examine
the transmitted light through a polaroid sheet, patterns of light and dark fringes
will be observed (in color, if white light is used). The patterns move as stress is
applied to the sample, and by counting the fringes and seeing where most of them
are, one can determine what the stress is. Engineers use this phenomenon as a
means of finding the stresses in odd-shaped pieces that are difficult to calculate.
Another interesting example of a way of obtaining birefringence is by means
of a liquid substance. Consider a liquid composed of long asymmetric molecules
which carry a plus or minus average charge near the ends of the molecule, so that
the molecule is an electric dipole. In the collisions in the liquid the molecules will
ordinarily be randomly oriented, with as many molecules pointed in one direction
as in another. If we apply an electric fñeld the molecules will tend to line up,
and the moment they line up the liquid becomes birefringent. With two polaroid
sheets and a transparent cell containing such a polar liquid, we can devise an
arrangement with the property that light is transmitted only when the electric
fñeld is applied. So we have an electrical switch for light, which is called a Kerr
ccli. 'This efect, that an electric field can produece birefringence in certain liquids,
is called the Kerr efect.
33-4 Polarizers
So far we have considered substances in which the refractive index is diferent
for light polarized in diferent directions. Of very practical value are those crystals
and other substances in which not only the index, but also the coefficient of
absorption, 1s diferent for light polarized in diferent directions. By the same
arguments which supported the idea of birefringence, it is understandable that
absorption can vary with the direction in which the charges are forced to vibrate
in an anisotropic substance. Tourmaline is an old, famous example and polaroid
is another. Polaroid consists of a thin layer oŸ small crystals of herapathite (a
salt oŸ iodine and quinine), all aligned with their axes parallel. 'These crystals
absorb light when the oscillations are in one direction, and they do not absorb
appreciably when the oscillations are in the other direction.
--- Trang 577 ---
Suppose that we send light into a polaroid sheet polarized linearly at an
angle Ø to the passing direction. What intensity will come through? This incident
light can be resolved into a component perpendicular to the pass direction which
1s proportional to sinØ, and a component along the pass direction which 1s
proportional to cosØ. “The amplitude which comes out of the polaroid is only
the cosine Ø part; the sin Ø component is absorbed. The amplitude which passes
through the polaroid is smaller than the amplitude which entered, by a factor cos Ø.
'The energy which passes through the polaroid, i.e., the intensity of the light, 1s
proportional to the square of cos Ø. Cos? 6, then, is the intensity transmitted
when the light enters polarized at an angle Ø to the pass direction. The absorbed
intensity, of course, is sỉn? 0.
An interesting paradox is presented by the following situation. We know that
1E is not possible to send a beam oŸ light through ©wo polaroid sheets with their
axes crossed at right angles. But if we place a third polaroid sheet betueen the
first two, with Its pass axis at 45° to the crossed axes, some light is transmitted.
W© know that polaroid absorbs light, it does not create anything. Nevertheless,
the addition of a third polaroid at 45° allows more light to get through. 'Phe
analysis of this phenomenon is left as an exercise for the student.
One of the most interesting examples of polarization is not in complicated
crystals or dificult substances, but in one of the simplest and most familiar of
situations—the refection of light from a surface. Believe it or not, when light is
refected om a glass surface it may be polarized, and the physical explanation of
this is very simple. It was discovered empirically by Brewster that light reflected
from a surface is completely polarized if the reflected beam and the beam refracted
into the material form a right angle. The situation is illustrated in Eig. 33-4. If
the ineident beam is polarized in the plane of incidence, there wiïll be no refection
at all. Only ïf the incident beam is polarized normal to the plane of ineidenece will
1E be refected. The reason is very easy to understand. In the reflecting material
the light is polarized transversely, and we know that it is the motion of the charges
in the material which generates the emergent beam, which we call the refected
beam. 'Phe source of this so-called reflected light is not simply that the incident
beam is reflected; our deeper understanding of this phenomenon tells us that the
ineident beam drives an oscillation of the charges in the material, which in turn
generates the reflected beam. FErom Eig. 33-4 it is clear that only oscillations
normal to the paper can radiate in the direction of refection, and consequently the
refected beam will be polarized normal to the plane of incidence. If the ineident