electric field, one can convince himself that the existence of optical activity and the sign of the rotation are independent of the orientation of the molecules. Corn syrup is a common substance which possesses optical activity. The phenomenon is easily demonstrated with a polaroid sheet to produce a linearly polarized beam, a transmission cell containing corn syrup, and a second polaroid sheet to detect the rotation of the direction of polarization as the light passes through the corn syrup 33-6 The intensity of reflected light Let us now consider quantitatively the reflection coefficient as a function of angle. Figure 33-6(a)shows a beam of light striking a glass surface, where it is partly reflected and partly refracted into the glass. Let us suppose that the incident beam,of unit amplitude, is linearly polarized normal to the plane of the paper. We will call the amplitude of the reflected wave b, and the amplitude of the re fracted wave a. The refracted and reflected waves will, of course, be linearly polarized, and the electric field vectors of the incident, reflected, and refracted waves are all parallel to each other. Figure 33-6(b)shows the same situation, but now we suppose that the incident wave, of unit amplitude, is polarized in the plane of the paper. Now let us call the amplitude of the reflected and refracted wave B and A, respectively We wish to calculate how strong the reflection is in the two situations illus- trated in Fig. 33-6(a)and 33-6(b ). We already know that when the angle between Fig. 33-6. An incident wave of unit the reflected beam and refracted beam is a right angle there will be no reflected amplitude is refected and refracted at a e if we cannot get a quantitative answer--an glass surface. In (a)the incident wave exact formula for B and b as a function of the angle of incidence, 1. nearly polarized normal to the plane of The principle that we must understand is as follows. The currents that are the paper In( b)the incident wave is generated in the glass produce two waves. First, they produce the reflected wave. linearly polarized in the direction shown Moreover, we know that if there were no currents generated in the glass, the in cident wave would continue straight into the glass. Remember that all the sources in the world make the net field. The source of the incident light beam produces a field of unit amplitude which would move into the glass along the dotted line in the figure. This field is not observed, and therefore the currents generated in the Using this fact, we will calculate the amplitude of the refracted waves, a andze In Fig. 33-6(a)we see that the field of amplitude b is radiated by the motion of charges inside the glass which are responding to a field a inside the glass, and that therefore b is proportional to a. We might suppose that since our two figures are exactly the same, except for the direction of polarization, the ratio B/A would be the same as the ratio b/a. This is not quite true, however, because in Fig. 33-6(b) the polarization directions are not all parallel to each other, as they are in Fig. 33-6(a). It is only the component of A which is perpendicular to B, A cos (i+ r), which is effective in producing B. The correct expression for the proportionality 33.1 a A cos(i+ r) Now we use a trick. We know that in both(a)and(b)of Fig 33-6 the electric field in the glass must produce oscillations of the charges which generate a field of amplitude-1, polarized parallel to the incident beam, and moving in the direction of the dotted line. But we see from part(b)of the figure that only the component of a that is normal to the dashed line has the right polarization to produce this field, whereas in Fig. 33-6(a)the full amplitude a is parallel to the polarization of the wave of amplitude -1. Therefore we can write the two amplitudes on the left side of Eq. (33. 2)each produce the wave of litude-l