eam 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 olarized in a direction perpendicular to the axis of the polaroid is strongly sorbed. 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 aroid is also useful in detecting the di polarized beam, or in determining whether a beam is linearly polarized or not One simply passes the beam of light through the polaroid sheet and rotates the polaroid in the plane normal to the beam. If the beam is linearly polarized, it will lot 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. If the transmitted in tensity is independent of the orientation of the polaroid, the beam is not linearly polarized Fig. 33-3. An experimental demon- To demonstrate the birefringence of cellophane, we use two sheets of polaroid stration of the birefringence of cellophane. as shown in Fig. 33-3. The first gives us a linearly polarized beam which we pass The electric vectors in the light are indi- through the cellophane and then through the second polaroid sheet, which serves cated by the dotted lines. the pass axes to detect any effect the cellophane may have had on the polarized light passing of the polaroid sheets and optic axes of through it. If we first set the axes of the two polaroid sheets perpendicular to each the cellophane are indicated by arrows. other and remove the cellophane, no light will be transmitted through the second The incident beam is unpolarized 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. These orientations in which linearly polarized light is transmitted through the cellophane with no effect on the direction of polarization must be the directions parallel and per pendicular to the optic axis of the cellophane sheet We suppose that the light passes through the cellophane with two different velocities in these two different orientations, but it is transmitted without changing the direction of polarization. When the cellophane is turned halfway between orientations, as shown in Fig. 33-3, we see that the light transm through the second polaroid is bright It just happens that ordinary cellophane used in commercial packa very close to a half-wave thickness for most of the colors in white ligh heet will turn the axis of linearly polarized light through 90 if the linearly polarized beam makes an angle of 45o 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 If 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 trans mitted depends on the thickness of the cellophane sheet, and we can vary the effective thickness of the cellophane by tilting it so that the light passes through the cellophane at an angle, consequently through a longer path in the cellophane As he sheet is tilted the transmitted color changes. With cellophane of different thicknesses one can construct filters that will transmit different colors. these filters have the interesting property that they transmit one color when the two polaroid sheets have their axes perpendicular, and the complementary color when of the two polaroid sheets are parallel Another interesting application of aligned molecules is quite practical Certain plastics are composed of 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 when the material is solidified, so the material is not perfectly homo