THE optical phenomenon presented by many gem-stones is complicated by their property of splitting up a beam of light into two with, in general, differing characters. In this chapter we shall discuss the nature of double refraction, as it is termed, and methods for its detection. The phenomenon is not one that comes within the purview of everyday experience. So long ago as 1669 a Danish physician, by name Bartholinus, noticed that a plate of the transparent mineral which at that time had recently been brought over from Iceland, and was therefore called “Iceland-spar,” possessed the remarkable property of giving a double image of objects close to it when viewed through it. Subsequent investigation has shown that much crystallized matter is doubly refractive, but in calcite—to use the scientific name for the species which includes Iceland-spar—alone among common minerals is the phenomenon so conspicuous as to be obvious to the unaided eye. The apparent separation of the pair of images given by a plate cut or cleaved in any direction depends upon its thickness. The large mass, upwards of two feet (60 cm.) in thickness, which is exhibited at the far end of the Mineral Gallery of the British Although none of the gem-stones can emulate calcite in this character, yet the double refraction of certain of them is large enough to be detected without much difficulty. In the case of faceted stones the opposite edges should be viewed through the table-facet, and any signs of doubling noted. The double refraction of sphene is so large, viz. 0·08, that the doubling of the edges is evident to the unaided eye. In peridot (Fig. 24), zircon (b), and epidote the apparent separation of the edges is easily discerned with the assistance of an ordinary lens. A keen eye can detect the phenomenon even in the case of such substances as quartz with small double refraction. It must, however, be remembered that in all such stones the refraction is single in certain directions, and the amount of double refraction 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 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 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 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 In the examination of a faceted stone, of the most usual shape, the simplest method is to lay the large facet, called the table, on a glass slip and view the stone through the small parallel facet, the culet. Should the latter not exist, it may frequently happen that owing to internal reflection no light emerges through the steeply inclined facets. This difficulty is easily overcome by immersing the stone in some highly refracting oil. A glass plate held by hand over the stone with a drop of the oil between it and the plate serves the purpose, and is perhaps a more convenient method. A stone which does not possess a pair of parallel facets should be viewed through any pair which are nearly parallel. We have stated that a plate of glass has no effect on the field. Suppose, however, it were viewed when placed between the jaws of a tightened vice An examination in convergent light is sometimes of service. An auxiliary lens is placed over the condenser so as to converge the light on to the stone. Light now traverses the stone in different directions; the more oblique the direction the greater the distance traversed in the stone. If it be doubly refractive, in any given direction there will be in general two rays with differing refractive indices and the resulting effect is akin to the well-known phenomenon of Newton’s rings, and is an instance of what is termed interference. It may be mentioned that the interference of light (Fig. 28) explains such common phenomena as the colours of a soap-bubble, the hues of tarnished steel, the tints of a layer of oil floating on water, and so on. Light, after diverging from the stone, comes to focus a little beneath the plane in which the image of the stone is formed. An auxiliary lens must, therefore, be inserted to bring the focal planes together, so that the interference picture may be viewed by means of the same eyepiece. If a uniaxial crystal be examined along the crystallographic axis in convergent light an interference picture will be seen of the kind illustrated on Plate III. The arms of a black cross meet in the centre of the field, which is surrounded by a series of circular rings, coloured in white light. Rotation A biaxial substance possesses two directions (the optic axes) along which a single beam is transmitted. If such a stone be examined along the line bisecting the acute angle between the optic axes (the acute bisectrix) an interference picture[4] will be seen which in particular positions of the stone with respect to the crossed nicols takes the forms illustrated on Plate III. As before, there is a series of rings which are coloured in white light; they, however, are no longer circles but consist of curves known as lemniscates, of which the figure of 8 is a special form. Instead of an unchangeable cross there are a pair of black “brushes” which in one position of the stone are hyperbolÆ, and in that at right angles become a cross. On rotating the stone we find that the rings move with it and are unaltered in form, whereas the brushes revolve about two points, called the “eyes,” where the optic axes emerge. If the observation were made along the obtuse bisectrix the angle between the optic axes would probably be too large for the brushes to come into the field, and the rings might not be visible in white light, though they would appear in monochromatic light. In the case of a substance like sphene the figure is not so simple, because the positions of the optic axes vary greatly for the different colours and the result is exceedingly complex; in monochromatic light, however, the usual figure is visible. It would probably not be possible in the case of There is yet another remarkable phenomenon which must not be passed over. Certain substances, of which quartz is a conspicuous example and in this respect unique among the gem-stones, possess the remarkable property of rotating the plane of polarization of a ray of light which is transmitted parallel to the optic axis. If a plate of quartz be cut at right angles to the axis and placed between crossed nicols in white light, the field will be coloured, the hue changing on rotation of one nicol with respect to the other. Examination in monochromatic light shows that the field will become dark after a certain rotation of the one nicol with respect to the other, the amount of which depends on the thickness of the plate. If the plate be viewed in convergent light, an interference picture is seen as illustrated on Plate III, which is similar to, and yet differs in some important particulars from the ordinary interference picture of a uniaxial stone. The cross does not penetrate beyond the innermost ring and the centre of the field is coloured in white light. If a stone shows such a picture, it may be safely assumed to be quartz. It is interesting to note that minerals which possess this property have a spiral arrangement of the constituent atoms. It has already been remarked (p. 28) that if a faceted doubly refractive stone be rotated with one facet always in contact with the dense glass of the refractometer the pair of shadow-edges that are The character of the refraction of gem-stones is given in Table V at the end of the book. |