POLARIZATION AND ELECTROMAGNETIC THEORY In our review of the history of optics we described some of the earlier work on polarization, and we must now make its character clearer. The phenomena of interference and diffraction were all explained by regarding the light as a wave, leaving it entirely open what it is that vibrates and how it does it. In fact all that we have so far said would, with suitable changes of scale, be just as true for sound as for light. But when we come to the phenomena of double refraction, this is not so; they are only explicable if the vibrations are transverse: Though we saw that, in spite of many attempts, no material model could be found which would carry waves in the way that aether does light, still it is quite possible to visualize polarization. A string stretched horizOntally may vibrate in a vertical or horizontal plane or simultaneously in both ; at any instant a point of the string is displaced from its position of rest in a direction perpendicular to the line of the wire, and this posi tion can be indicated by drawing a line in the direction and of the length of the displacement. When a light-wave is travelling through space, we can also represent it at any point and time by drawing a line in a definite direction and of a definite length. It should be explained that, unlike the case of the string, here the length is only diagrammatic and can be represented on any scale, as long as we are consistent and adopt the same scale for other points. This line is called the light-vector, and the wave is said to be trans verse, because the light-vector is always found to be at right-angles to the direction of the wave, that is to say it lies somewhere in the plane of the wave-front. The reason for this will appear when we come to the electromagnetic theory ; we shall first describe the main properties of polarization without justifying them.
if A =o we have light plane polarized in the direction y. If we have a= j3, we see that at any time Y/X=B/A, so that again we have plane polarized light, in direction arc tanB/A and with amplitude -\/ . Next consider the case B= A, j3 = a -F: Then so that the vector describes a circle; this is therefore called circularly polarized light. In the general case we can find the locus of the light-vector by eliminating t and get This is an ellipse of which the axes are determined as to position and magnitude by A, B and a —(3. The most general type of light is therefore called elliptically polarized, and we recognize our previous types as degenerate ellipses.
We next consider the propagation of such waves, that is to say, the phase relations of the light-vectors for different positions of the wave-front. Our wave is now written as and the character of the polarization is the same for all values of z, as it will depend on A, B and Next we take I as fixed and consider the way the light-vector is arranged for various values of z. We may liken it to the stretched string. If B=o it will be in the shape of a sine-curve in the plane of xz with wave-length c/v, and similarly whenever a= )3, though for a different plane. If (3=a and B= A, the locus is a screw, or helix, of radius A and pitch equal to the wave length c/v. If the axes are right-handed (so that a man standing with his head towards z has x to his right and y to his left), then the screw may be seen to be left-handed. This is therefore called left-handed circularly polarized light. If we take =a 2 instead, we should get a right-handed screw. The distinction between right and left-handed circularly polarized light is physi cally very important, as it plays a leading part in the phenom enon of gyration.. In the case of elliptically polarized light, the locus of light-vectors may be described as a flattened screw; it may be either right- or left-handed again, but the question is not so important physically. This suffices to describe the form of the waves, and it only remains to define the intensity. At any point this is given as the average value of the square of the light-vector ; in the cases we have con sidered it is the average of When the waves are 'travelling in an arbitrary direction instead of along z, we may have three components of the light-vector, and in such a case is to be aver aged over the time.