Page:Encyclopædia Britannica, Ninth Edition, v. 14.djvu/632

 612 LIGHT Reflex ion not at the polar izing angle, Polar ization by ordi nary re fraction. Nicol s prism. thousands of wave-lengtbs more than the other. But, thirdly, the fact, that, when homogeneous light is used, Newton s rings have been counted up to the 7000th shows that, whatever be the actual nature of the vibrations of unpolarized light, they must for at least 7000 waves in succession be almost precisely similar to one another. Then, for other 7000 waves or so, we may have a totally different type of vibration. But, fourthly, in the course of yth of a second, at the very utmost, the vibrations must have been almost uniformly distributed over all directions perpendicular to the ray. Again, however, fifthly, another quite different view may be suggested. All common light has its origin from a practically infinite number of sources, consisting of the vibrating particles of the luminous body. The contributions from each of these sources (so far as one definite wave-length is concerned) may be and probably are at any one point as different in direction of vibration as they certainly must be in phase. 1 From this point of view, which we cannot develop here, the uniformity of optical phenomena becomes quite analogous to the statistical species of uniformity which is now found to account for the behaviour of the practically infinite group of particles forming a cubic inch of gas. The reader need only think of the fact that, so numerous are those particles, it is practically (though not theoreti cally) impossible that even a cubic millimetre of air should, even for y^^th of a second, contain oxygen particles alone. When light is reflected at an incidence either less or greater than the polarizing angle, it behaves as if part of it only were polarized and the rest ordinary light ; and it is said to be partially polarized. Tested by a crystal of Iceland spar, it gives two images in all positions of the crystal ; but their brightness is unequal except in the special positions where they would be of equal brightness were the ray wholly polarized. From the fourth of the remarks made above regarding common light, and the facts of double refraction, it follows at once that, when light is to any extent polarized by reflexion, there must be an exactly equal amount of polarized light in the refracted ray, and its plane of polarization must be perpendicular to that of refraction. This was established by experiment soon after Malus s discovery. But as the reflected ray from glass, water, &c., is in general much weaker than the refracted ray, the percentage of polarized light is generally much greater in the former. It was found, however, by experiment that refraction at a second glass plate parallel to the first increases the proportion of polarized to common light in the transmitted ray, and thus that light may be almost completely polarized by transmission, at the proper angle, through a number of parallel plates. The experimental data of this subject were very carefully obtained by Brewster. He has found, for instance, how the angle of incidence for the most complete polarization varies with the number of plates. The plane of polarization of such a bundle is perpendicular to the plane of refraction. This, however useful on many occasions, is at best a rough arrangement for producing polarized light. By far the most perfect polarizer for a broad beam of light is a crystal of Iceland spar, sufficiently thick to allow of the complete separation of the two rays. But such specimens are rare and costly, so that the polarizer in practical use is now what is called Nicol s prism, invented in 1828 (Jameson s Journal, p. 83). By cutting a rhomb of Iceland spar in two, and cementing the pieces together with Canada balsam (after carefully polishing the cut faces), 1 A curious exception occurs in the case of light radiated from a body which polarizes by absorption. See RADIATION. Nicol produced an arrangement in which one only of the two rays is transmitted, the other being totally reflected at the surface of the balsam. The reason is simply that the refractive index of Canada balsam is intermediate to those of the ordinary and extraordinary rays in the spar. The ordinary ray, falling very obliquely on a medium of a smaller refractive index, is totally reflected ; the extra ordinary ray, falling on a medium of greater, but very little greater, refractive power, is almost wholly transmitted. The only defect of the Nicol s prism is that, to secure the total reflexion, its length must be considerably greater than its breadth ; and thus it necessarily limits the diver gency of the beam it allows to pass. Certain doubly refracting crystals exert considerable Polar- absorption on one of the two rays they produce, and can ization therefore, when in plates of sufficient thickness, be by ^ employed as polarizers. This is the case with some S specimens of tourmaline when cut into plates parallel to the axis of the crystal. It is also found in the flat crystals of several artificial salts, such as, for instance, iodo-sulphate of quinine. Let us now suppose that by one or other of these pieces Two of apparatus, say a Nicol s prism, light has been polarized. Nicols, If we examine this ray by means of a second Nicol, placed in a similar position to the first, it passes practically unaltered. As the second Nicol is made to rotate, more and more of the light is stopped, till the rotation amounts to a right angle. Two well-constructed Nicols, placed in this position, are practically opaque to the strongest sunlight. During the next quadrant of rotation the transmitted ray gradually increases in brightness, until at 180 of rotation it passes practically unaltered. Precisely the same phenomena occur in the same order during the next half of a complete rotation. The reader will observe that this is merely Huygens s original statement, limited to one of the four rays which are produced by passing common light successively through two crystals of Iceland spar. Whatever be the true mechanism of polarized light, Sym- there can be no doubt that its vibrations are symmetrical metl T with respect to the ray, and also with respect to the plane Pl arize of polarization. Hence we may, for many important purposes, symbolize them by simple harmonic vibrations taking place either in or perpendicular to the plane of polarization. But, if they be supposed to take place simultaneously in these two planes, their quality or nature must be essentially different in the two, else the symmetry above referred to would be violated. Hence it will be sufficient for the present to assume that they take place perpendicular to the plane of polarization. The nature of the resulting effects, so far as the eye is concerned, will not be different for the different hypotheses. Also, as no instance has yet been observed, even with the most intense beams of light, in which the joint effects observed are not those due to simple superposition, we may assume that the elastic force of the luminiferous medium, called into play by a displacement, is directly proportional to the displacement, and therefore that the vibrations for each wave-length follow the simple harmonic law, that of the cycloidal pendulum. The subject of the composition of simple harmonic motions of equal period falls to be discussed as an im portant branch of kinematics (see MECHANICS). We will therefore here assume the following results, referring to the above-quoted article for their proof : 1. Two simple harmonic motions of the same period, in Proper- lines perpendicular to one another, give, in general, elliptic t ! es ^ motion, which may be in the positive or negative direction &quot;^oiJ of rotation. _ motion. 2. The ellipse becomes a straight line, and the resultant motion therefore simple harmonic, when the phases of the