We have represented all the various polarization cases in Figs.33-1 and 33-2 as superpositions of two special polarization cases, namely x and y in various amounts and phases. Other pairs could equally well have been used. Polarization along any two perpendicular axes x', y' inclined to x and y would serve as well for example, any polarization can be made up of superpositions of cases(a)and 人 (e)of Fig 33-2]. It is interesting, however, that this idea can be extended to other cases also. For example, any linear polarization can be made up by superposing suitable amounts at suitable phases of right and left circular polarizations(cases (c)and(g)of Fig. 33-2], since two equal vectors rotating in opposite directions add to give a single vector oscillating in a straight line(Fig. 33-8). If the phase of one is shifted relative to the other, the line is inclined. Thus all the pictures of Fig 33-1 could be labeled"the superposition of equal amounts of right and left circularly polarized light at various relative phases. As the left slips behind the right in phase, the direction of the linear polarization changes. Therefore optically Fig 33-8. Two oppositely active materials are, in a sense, birefringent, Their properties can be described by vectorsof equal amplitude add to saying that they have different indexes for right- and left-hand circularly polarized a vector in a fixed direction but light. Superposition of right and left circularly polarized light of different intensi- ties produces elliptically polarized light Circularly polarized light has another interesting property--it carries angular momentum(about the direction of propagation). To illustrate this, suppose that such light falls on an atom represented by a harmonic oscillator that can be dis- placed equally well in any direction in the plane xy. Then the x-displacement of the electron will respond to the E component of the field, while the y-component responds, equally, to the equal Ey component of the field but 90 behind in phase That is, the responding electron goes around in a circle, with angular velocity in response to the rotating electric field of the light(Fig. 33-9). Depending on the damping characteristics of the response of the oscillator, the direction of the displacement a of the ele lectron, and the direction of the force gee on it need not be the same but they rotate around together. The E may have a component at right angles to a, so work is done on the system and a tor rque T is exerted. The per second is Tw. Over a period of time T the energy absorbed is TT, while T is the angular momentum delivered to the matter absorbing the energy. We see therefore that a beam of right circularly polarized light containing a total energy g carries an angular momentum(with vector directed along the direction of prop Fig 33-9. A charge moving in agation)&/w. For when this beam is absorbed that angular momentum is de circle in response to circularly polarized livered to the absorber. Left-hand circular light carries angular momentum of the opposite sign, -8/w