Polarization 33-1 The electric vector of light In this chapter we shall consider those phenomena which depend on the fac 33-1 The electric vector of light that the electric field that describes the light is a vector. In previous chapters have not been concerned with the direction of oscillation of the electric field, except 33-2 Polarization of scattered light to note that the electric vector lies in a plane perpendicular to the direction of 33-3 Birefringence propagation. The particular direction in this plane has not concerned us. We 33-4 Polarizers now consider those phenomena whose central feature is the particular direction of oscillation of the electric field 33-5 Optical activity In ideally monochromatic light, the electric field must oscillate at a definite frequency, but since the x-component and the y-component can oscillate independ 33-6 The intensity of reflected light ently at a definite frequency, we must first consider the resultant effect produced 33-7 Anomalous refraction by superposing two independent oscillations at right angles to each other. what kind of electric field is made up of an x-component and a y-component which oscillate at the same frequency? If one adds to an x-vibration a certain amount of y-vibration at the same phase, the result is a vibration in a new direction in the xy-plane. Figure 33-1 illustrates the superposition of different amplitudes for the x-vibration and the y-vibration. But the resultants shown in Fig. 33-1 are not the only possibilities; in all of these cases we have assumed that the x-vibration and the y-vibration are in phase, but it does not have to be that way. It could be that the x-vibration and the y-vibration are out of phase y ry y Kx Fig. 33-1. Superposition of x-vibrations and y-vibrations in phase When the x-vibration and the y-vibration are not in phase, the electric field vector moves around in an ellipse, and we can illustrate this in a familiar way. If we hang a ball from a support by a long string, so that it can swing freely in a horizontal plane, it will execute sinusoidal oscillations. If we imagine horizontal x-and y-coordinates with their origin at the rest position of the ball, the ball can swing in either the x- or y-direction with the same pendulum frequency. By selecting the proper initial displacement and initial velocity, we can set the ball in oscillation along either the x-axis or the y-axis, or along any straight line in the xy-plane. These motions of the ball are analogous to the oscillations of the electric field vector illustrated in Fig. 33-1. In each instance, since the x-vibrations and the y-vibrations reach their maxima and minima at the same time, the x-and y-os- cillations are in phase. But we know that the most general motion of the ball is motion in an ellipse, which corresponds to oscillations in which the x-and y-directions are not in the same phase. The superposition of x-and y-vibrations which are not in phase is illustrated in Fig. 33-2 for a variety of angles between the phase of the x-vibration and that of the y-vibration. The general result is that the electric vector moves around an ellipse. The motion in a straight line is a particular