In order that we may arrive at some ideas as to the nature of polarization, we must consider on the basis of the undulatory theory of light (q.v.) how a ray of light can have sides. If we take, for a comparison, waves of sound, as we know that in them (Soum)) the particles of air move back and forward in the 1:.ne in which the sound travels, we see that a beam of sound cannot possibly have sides, since the motions of the particles of air in it are precisely the same from whatever side we consider them. Next take waves In water, where we see the water rising and falling as the undulation (not the water) travels uniformly onward in a horizontal direction; and this at once gives the required analogy. So far as phenomena of interference (q.v.; see also DIFFuaarroN) are con cerned, waves, whether in air or in water, present them, so that they merely show us that light depends on undulations, but not the kind of undulation. But when, from the facts of polarization, we find that a ray of light can have sides, we see that the vibra tions of the luminiferOUS medium must be tretteyvee to the direction of the •ray. Common light,'then, consists of vibrations which take place indifferently and in succession in all directions transverse to that of the ray; while light which is completely polarized has its vibrations limited to a particular transverse direction. A `Nicol's prism allows no light to pass through it except that which vibrates in a particular transverse direction, depending upon the position of the axes of the pieces of Iceland spar of %vhicli it is made Light which has passed through one Nicol's prism is sifted so as to contain none but such transverse vibrations, and will of course pass freely through a second prism, or be com pletely or partially stopped by it; according as the two prisms are similarly situated, or turned so that the directions of the vibrations they can transmit are inclined at right angles. or at any other angle.
It is not yet settled what the direction of these vibrations is in any particular case; whether they take place in, or perpendicular to, the plane of polarization; and the point is extremely important in the theory of the subject, though not to the explanation of the ordinary experimental results. To explain the nature of this difficulty, we merely men tion the simple case of polarization by reflection at a glass plate. Do the vibrations of the reflected ray take place'popendicular to the plane of reflection (i.c., parallel to the reflecting surface), or do they take place in the plane of reflection? Some high authori ties are in favor of the latter hypothesis, but the general opinion of scientific men at present unquestionably leans to the former. ,Many delicate experiments have been made to decide the question, but their results have been irreconcilable with each other. From the results which we have just arrived at, it is evident that the or vibrations of the luminiferous medium, of which light consists, are similar to those of the bob of a pen dulum (q.v.), the ray in Ibis case being supposed to proceed vertically downwards. Polar ized light consists of vibrations analogous to those of the ordinary pendulum, backward at:d forward in a line. But we have seen that any motion of the pendulum may be compounded of two such motions in planes perpendicular to each other. This is analogous to the decom position of common light by a doubly-refracting crystal into two rays polarized at right angles. But we tind in nature, and can produce artificially, motions of the Itiminiferous
medium resembling exactly the elliptic, and circular motions of the (conical) pendulum. They occur in nature in all cases of reflection from metallic surfaces, and also from the surfaces of highly refractive bodies, such as diamond, etc. The easiest artificial method of procuring them is to allow polarized light to pass through a thin plate of a doubly refracting crystal, such as a film of mica. Thus if OA be the direction of vibration of the polarized light, the ray moving perpendicularly to the paper Oa, Ob, the directions (at right angles to each other) of vibration of the two rays into which it is divided by the mica, we have only to let fall from A perpen diculars on On and Ob to determine the extent of the resolved vibrations in these directions. Now if the two rays moved equally rapidly through the mica, they would simply recombine on leaving it into a single plane polarized ray, whose vibrations would be represented by OA as before. But, in general, one of the rays is retarded more than the other, and the combination of two such oscillations is seen by geometrical considerations to give an ellipse whose center is at 0, and which touches each side of the rectangle of which Aa and Ab are half sides. The limiting forms of these ellipses are, of course, the diagonals of the rectangle; so that there are two'cases for the light remaining plane polarized after passing a the mica, for an infinite number in which it will be elliptically polarized. Also the difference of retardation of the two rays may be such as to correspond to a description of these ellipses either right-handedly or the opposite. In particular cases the ellipse may be a circle; then it is obvious that the rectangle must become a square, that the directions of vibration of the two rays in the mica must be equally inclined to that of the original polarized ray, and that one ray must be retarded an odd number of quarter oscillations more than the other. If it be 1, 5, 9, etc., quarter oscillations, the rotation is in one direction; if 8, 7, 11, etc., it is in the opposite. Circularly polarized light cannot be distinguished by the eye, even with the help of a Nicol's prism, from common light; but by the interposition of a thin plate of a doubly refracting crystal, phenomena are produced which common light cannot give. Before we leave this part of the subject, it may be remarked that the composition of two equal and opposite circular vibrations produces a plane vibratian, whose plane depends upon the simultaneous positions of the revolving bodies in their circular orbits. Hence a plane polarized ray may always be considered as made up of two circularly polarized rays, and if these pass through a medium which retards one more than the other, the plane of polarization of their resultant, when they leave the medium, will in general not be the same as that of the incident ray. In other words, the plane of polar ization will have been caused to rotate through a certain angle, which will be propo• tional to the difference of retardation of its circular components. This is the explanation of what Blot called roteamwpu/arisation in quartz, turpentine, sugar, etc., and of the rotation of the plane of polarization discovered by Faraday when a polarized ray passes through a transparent body under the action of a magnet.