Crystals

by A. E. H. Tutton

If a second prism be cut complementarily to the first, that is, so that the refracting edge is parallel to the third axis of the ellipsoid (the direction of transmission through the first prism) and the bisecting plane again parallel to one of the three axial planes of the ellipsoid, such a prism will also yield two refracted images corresponding to two indices; one of them, that particular image the vibrations of which are parallel to the refracting edge, will correspond to that one of the three principal indices which was not given by the first prism, while the other one will afford a duplicate determination of one of the two indices afforded by the first prism. Hence, a couple of such axially orientated prisms of a rhombic, monoclinic, or triclinic crystal will enable us to determine all three refractive indices, and one of them in duplicate, which latter fact will enable us to check the accuracy of our work.

If the 60°-prism be cut from a crystal of the uniaxial group, that is, from a hexagonal, tetragonal, or trigonal crystal—quartz or calcite being admirable examples of the latter and particularly suitable for demonstration purposes—it will generally afford two spectra in the same manner as a crystal of the three birefringent systems of lower symmetry. But there is one special mode of cutting which results in the prism exhibiting only a single spectrum, namely, when the hexagonal, tetragonal, or trigonal axis of symmetry, which is also the unique “optic axis” of the crystal along which there is no double refraction, is arranged to be perpendicular to the bisecting plane of the 60°-prism. For then the light is transmitted along this unique axial direction when the prism is arranged for the minimum deviation of the refracted rays out of their original path, and as it may vibrate in any direction perpendicular thereto with equal velocity there is no separation into two rays, that is, no double refraction, and thus only a single spectrum is afforded by such a prism in white light, or a single image of the slit in monochromatic light, and this latter will at once yield the refractive index which is generally indicated conventionally by the letter ω, corresponding to light vibrations perpendicular to the axis.

Spectroscopists take advantage of this interesting fact, when they employ a train of quartz prisms so cut in order to explore the violet and ultra-violet region of the spectrum; for quartz transmits many of the ultra-violet rays which glass absorbs. Each prism gives only a single image like glass, whereas if it were otherwise cut it would give two spectra, which would so complicate matters as to render quartz useless for the purpose.

When the prism of quartz or calcite, or of any hexagonal, tetragonal, or trigonal substance, is cut so that the rays of light are transmitted through it perpendicularly to the axis, and so that the refracting edge is parallel to the axis, the light is broken up into two rays, one of which is composed of light vibrating parallel to the edge and therefore to the axis, and the other of light vibrating perpendicularly to the axis. Such a prism consequently affords the two principal extreme refractive indices of the crystal, ω and ε, the latter letter being always assigned to the refractive index of a uniaxial crystal corresponding to vibrations parallel to the axis.

A uniaxial crystal, one belonging to the hexagonal, tetragonal, or trigonal systems, has thus two principal refractive indices, ω and ε, while a biaxial crystal, one belonging to the rhombic, monoclinic, or triclinic systems of symmetry, has three, α, β, γ, corresponding to vibrations respectively parallel to the three rectangular axial directions of the optical ellipsoid, which are also the crystallographic axial directions in the case of a rhombic crystal. The index α is the minimum, and γ the maximum refractive index,the β index being intermediate; when the latter lies nearer to α in value, the crystal is said to be a positive one, but when nearer to γ the crystal is conventionally supposed to be negative. Similarly, when in a uniaxial crystal ε is the greater, as it is in the case of quartz, the crystal is termed positive, but if ω be the greater index, as happens in the case of calcite, then the crystal is by convention considered negative.

Just as in the case of gypsum, which is a positive biaxial crystal (the reason for the term biaxial will presently be more fully explained), when the two spectra afforded by a prism of calcite or quartz cut to afford both ε and ω are examined in plane polarised light, by introducing a Nicol prism somewhere in the path of the light, the two images corresponding respectively to ε and ω will be found to be produced by light polarised in two planes at right angles to each other. For when the Nicol is at its 0° position one will be extinguished, and when it is at 90° the other will be quenched. At the 45° position of the Nicol both images will be visible with their partial intensities, as happens also in the cases of biaxial prisms.

This behaviour of 60°-prisms of crystals belonging to the seven different styles of crystal architecture, as compared with a prism of glass or other transparent non-crystalline substance, is extremely instructive. For not only is the optical constant refractive index—the measure of the power exhibited by the crystal of bending light, corresponding to its effect in retarding by the nature of its internal structure the velocity of the light vibrations—the most important of all the optical constants, but also in the course of its determination we learn more of the behaviour of crystals towards light than from any other type of optical experiment.

Fig. 67.—Experiment to show Rectangular Polarisation of the two Spectra afforded by a 60°-Prism of a Doubly Refracting Crystal cut to afford two Indices of Refraction.

In Fig. 67 is shown a convenient mode of demonstrating the experiment with the aid of the electric lantern and one of the large Nicol prisms of the projection polariscope, already briefly described in Chapter VII. in connection with the Mitscherlich experiment. The 60°-prism is arranged on a small adjustable stand nearest the screen; then comes the Nicol polarising prism of 2½ to 3 inches clear aperture, behind which is the projecting lens, at the focus of which is placed the adjustable slit on a separate stand. The slit is filled with light from the condenser of the electric lantern, and in the lantern front a thick water cell is arranged, in order to remove sufficient of the heat rays which accompany the light beam to avoid damage to the balsam joint of the calcite Nicol. When all the parts are properly arranged a sharp image of the slit should first be thrown on the screen directly, in the temporary absence of the 60°-prism, and then on replacing the latter at the proper angle for minimum deviation, when the light traverses the prism parallel to its third unused side, a spectrum or pair of spectra—according to the position of the Nicol and to the nature of the 60°-prism as explained in the foregoing discussion of the possibilities—will be projected on a second screen (or the same one if movable) arranged at the proper angle to receive the refracted rays.