Gem-Stones and Their Distinctive Characters

by George Frederick Herbert Smith

Fig. 25.—Wave-Motion.

Before the discovery of the phenomenon of double refraction the foundation of the modern theory of light had been laid by the genius of Huygens. According to this theory light is the result of a wave-motion (Fig. 25) in the ether, a medium that pervades the whole of space whether occupied by matter or not, and transmits the wave-motion at a rate varying with the matter with which it happens to coincide. Such a medium has been assumed because it explains satisfactorily all the phenomena of light, but it by no means follows that it has a concrete existence. Indeed, if it has, it is so tenuous as to be imperceptible to the most delicate experiments. The wave-motion is similar to that observed on the surface of still water when disturbed by a stone flung into it. The waves spread out from the source of disturbance; but, although the waves seem to advance, the actual particles of water merely move up and down, and have no motion at all in the direction in which the waves are moving. If we imagine similar motion to take place in any plane and not only the horizontal, we form some idea of the nature of ordinary light. But after passing through a plate of Iceland-spar, light no longer vibrates in all directions, but in each beam the vibrations are parallel to a particular plane, the two planes being at right angles. The exact relation of the direction of the vibrations to the plane of polarization is uncertain, although it undoubtedly lies in the plane containing the direction of the ray of light and the perpendicular to the plane of polarization. The waves for different colours differ in their length, i.e. in the distance, 2 bb (Fig. 25), from crest to crest, while the velocity, which remains the same for the same medium, is proportional to the wave-length. The intensity of the light varies as the square of the amplitude of the wave, i.e. the height, ab, of the crest from the mean level.

Various methods have been proposed for obtaining polarized light. Thus Seebeck found in 1813 that a plate of brown tourmaline cut parallel to the crystallographic axis and of sufficient thickness (cf. [p. 11]) transmits only one ray, the other being entirely absorbed within the plate. Another method was to employ a glass plate to reflect light at a certain critical angle. The most efficient method, and that in general use at the present day, is due to the invention of Nicol. A rhomb of Iceland-spar (Fig. 26), of suitable length, is sliced along the longer diagonal, dd, and the halves are cemented together by means of canada balsam. One ray, ioo, is totally reflected at the surface separating the mineral and the cement, and does not penetrate into the other half; while the other ray, iee, is transmitted with almost undiminished intensity. Such a rhomb is called a Nicol’s prism after its inventor, or briefly, a nicol.

Fig. 26.—Nicol’s Prism.

If one nicol be placed above another and their corresponding principal planes be at right angles no light is transmitted through the pair. In the polarizing microscope one such nicol, called the polarizer, is placed below the stage, and the other, called the analyser, is either inserted in the body of the microscope or placed above the eyepiece, and the pair are usually set in the crossed position so that the field of the microscope is dark. If a piece of glass or a fragment of some singly refractive substance be placed on the stage the field still remains dark; but in case of a doubly refractive stone the field is no longer dark except in certain positions of the stone. On rotation of the plate, or, if possible, of the nicols together, the field passes from darkness to maximum brightness four times in a complete revolution, the relative angular intervals between these positions being right angles. These positions of darkness are known as the positions of extinction, and the plate is said to extinguish in them. This test is exceedingly delicate and reveals the double refraction even when the greatest difference in the refractive indices is too small to be measured directly.

Doubly refractive substances are of two kinds: uniaxial, in which there is one direction of single refraction, and biaxial, in which there are two such directions. In the case of the former the direction of one, the ordinary ray, is precisely the same as if the refraction were single, but the refractive index of the other ray varies from that of the ordinary ray to a second limiting value, the extraordinary refractive index, which may be either greater or less. If the extraordinary is greater than the ordinary refractive index the double refraction is said to be positive; if less, to be negative. A biaxial substance is more complex. It possesses three principal directions, viz., the bisectrices of the directions of single refraction and the perpendicular to the plane containing them. The first two correspond to the greatest and least, and the last to the mean of the principal indices of refraction. If the acute bisectrix corresponds to the least refractive index, the double refraction is said to be positive, and if to the greatest, negative. The relation of the directions of single refraction, s, to the three principal directions, a, b, c, is illustrated in Fig. 27 for the case of topaz, a positive mineral. The refractive indices of the rays traversing one of the principal directions have the values corresponding to the other two. In the direction a we should measure the greatest and the mean of the principal refractive indices, in the direction b the greatest and the least, and in the direction c the mean and the least. The maximum amount of double refraction is therefore in the direction b.

Fig. 27.—Relation of the two
Directions of single Refraction to
the principal Optical Directions
in a Biaxial Crystal.