33-2 Polarization of scattered light The first example of the polarization effect that we have already discussed is the scattering of light. Consider a beam of light, for example from the sun, shining on the air. The electric field will produce oscillations of charges in the air, and mo- tion 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. If we consider light scattered at 90 the vibration of the charged particles radiates to the observer only when the vibration is perpendicular to the observer's 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 effect of polarization is the fact that there are substances for which the index of refraction is different for light linearly polarized in one 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 field passes through this bstance? Suppose that because of the structure of the molecule, the electrons in the substance respond more easily to oscillations in the direction parallel to the axes of the molecules than they would respond if the electric field tries to push them at right angles to the molecular axis. In this way we expect a different response for polarization in one direction than for polarization at right angles to that direc- tion. Let us call the direction of the axes of the molecules the optic axis. When the polarization is in the direction of the optic axis the index of refraction is different than it would be if the direction of polarization were at right angles to it Such a substance is called birefringent. 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 birefringent? In a birefringent substance there molecules. Certainly a cubic crystal, which has the symmetry of a cube " metrical must be a certain amount of lining up, for one reason or another, of uns lot be birefringent. But long needlelike crystals undoubtedly contain molecules that are asymmetric, and one observes this effect very easily Let us see what effects we would expect if we were to shine polarized light through a plate of a birefringent substance. If the polarization is parallel to the optic axis, the light will go through with one velocity; if the polarization is per- pendicular to the axis, the light is transmitted with a different velocity. An inter esting situation arises when, say, light is linearly polarized at 45 to the optic axis Now the 45 polarization, we have already noticed, can be represented as a super position of the x- and the y-polarizations of equal amplitude and in phase, shown in Fig. 33-2(a). Since the x- and y-polarizations travel with different velocities, their phases change at a different rate as the light passes through the substance. So, although at the start the x- and y-vibrations are in phase, inside the material the phase difference between x-and y-vibrations is proportional to the depth in the substance. As the light proceeds through the material the polarization hanges as shown in the series of diagrams in Fig. 33-2. If the thickness of th plate is just right to introduce a 90 phase shift between the x-and y-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 difference between the x-and the y-polarizations. If linearly polarized light is sent through two quarter-wave plates, it will come out plane-polarized again, but at right angles to the original direction, as we can see from Fig. 33-2(e) One can easily illustrate this phenomenon with a piece of cellophane. Cello phane is made of long, fibrous molecules, and is not isotropic, since the fibers lie preferentially in a certain direction. To demonstrate birefringence we need a