geneous. However, if we apply tension to a piece of this plastic material, it is as if we were pulling a whole tangle of strings, and there will be more strings preferen tially aligned parallel to the tension than in any other direction. So when a stress applied to certain plastics, they become birefringent, and one can see the effects 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 d pieces that are difficult to calculate. Another interesting example of a way of obtaining birefringence is by means ce. Consider a liq 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 direc tion as in another. If we apply an electric field 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 field is applied. So we have an electrical switch for light, which is called a Kerr cell. This effect, that an electric field can produce birefringence in certain liquids, is called the Kerr effect 33-4 Polarizers So far we have considered substances in which the refractive index is different for light polarized in different directions. Of very practical value are those crystals and other substances in which not only the index, but also the coefficient of ab sorption, is different for light polarized in different directions. By the same argu- ments which supported the idea of birefringence, it is understandable that absorp tion 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 of small crystals of herapathite (a salt of 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 Suppose that we send light into a polaroid sheet polarized linearly at an angle 0 to the passing direction. What intensity will come through? This incident light can be resolved into a component perpendicular to the pass direction which is proportional to sin 0, and a component along the pass direction which is pro- portional to cos 8. The amplitude which comes out of the polaroid is only the cosine 0 part; the sin 0 component is absorbed. The amplitude which passes through the polaroid is smaller than the amplitude which entered, by a factor cos 0. The energy which passes through the polaroid, i.e., the intensity of the ght, is proportional to the square of cos e. Cos, then, is the intensity transmitte when the light enters polarized at an angle 6 to the pass direction. The absorbed An interesting paradox is presented by the following situation. We know that isis not possible to send a beam of light through two polaroid sheets with their axes crossed at right angles. But if we place a third polaroid sheet between the first two with its pass axis at 45 to the crossed axes, some light is transmitted We 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. The 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 difficult substances, but in one of the simplest and most familiar of ituations-the reflection of light from a surface. Believe it or not, when light is eflected from 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 33-s