case corresponding to a phase difference of zero(or an integral multiple of T) motion in a circle corresponds to equal amplitudes with a phase difference of 90o (or any odd integral multiple of T/2) In Fig, 33-2 we have labeled the electric field vectors in the x-and y-directions with complex numbers, which are a convenient representation in which to express the phase difference. Do not confuse the real and imaginary components of the complex electric vector in this notation with the x- and y-coordinates of the field The x-and y-coordinates plotted in Fig. 33-1 and Fig. 33-2 are actual electric fields that we can measure. The real and imaginary components of a complex electric field vector are only a mathematical convener and have no physic d ry e(a+1;:4x/s 1nc;1 cos(at.) -coB at;-I =-a(7};:1m/,at;- Fig. 33-2. Superposition of x-vibrations and y-vibrations with equal amplitudes but various relative hases. The components Es and Ey are expressed in both real and complex notations Now for some terminology. Light is linearly polarized(sometimes called plane polarized)when the electric field oscillates on a straight line; Fig.33- illustrates linear polarization. When the end of the electric field vector travels in an ellipse, the light is elliptically polarized. When the end of the electric field vector travels around a circle, we have circular polarization. If the end of the electric vector, when we look at it as the light comes straight toward us, goes around counterclockwise direction, we call it right-hand circular polarization igure 33-2(g)illustrates right-hand circular polarization, and Fig 33-2(c)shot left-hand circular polarization. In both cases the light is coming out of the paper. Our convention for labeling left-hand and right-hand circular polarization is consistent with that which is used today for all the other particles in physics which exhibit polarization (e.g, electrons). However, in some books on optics the pposite conventions are used he must be careful We have considered linearly, ally polarized light, whicl covers everything except for the case of unpolarized light. Now how can the light be unpolarized when we know that it must vibrate in one or another of these ellipses? If the light is not absolutely monochromatic, or if the x- and y-phases are not kept perfectly together, so that the electric vector first vibrates in one d i that one atom emits during 10-8 sec, and if one atom emits a certain polarization and then another atom emits light with a different polarization, the polarizations will change every 10-8 sec. If the polarization changes more rapidly than we can detect it, then we call the light unpolarized, because all the effects of the polarization average out. None of the interference effects of polarization would show up with unpolarized light. But as we see from the definition, light is unpolarized only if re are unable to find out whether the light is polarized or not