The intermediate refractive index β was found to be as under—
| For | red lithium light | 1.4496 |
| „ | yellow sodium „ | 1.4521 |
| „ | green thallium „ | 1.4545 |
The double refraction was also determined and found to be of positive sign.
The optical properties of calcium dextro-glycerate thus confirm absolutely the monoclinic nature of the symmetry, as regards the crystal system. And it was conclusively demonstrated by the goniometrical part of the investigation that the exterior symmetry was not such as agreed with holohedral monoclinic symmetry, but with that of the sphenoidal class, in which the only one of the two elements of monoclinic symmetry (the plane of symmetry and the digonal axis of symmetry) in operation is the digonal axis, thus leaving the two terminations of that axis, at opposite sides, right and left, of the possible symmetry plane, unsymmetrical. And this is precisely the symmetry which is characteristic of an enantiomorphous optically active substance.
Unfortunately, the corresponding lævo-salt has not yet been obtained in measurable crystals, but there can be no doubt that whenever such are forthcoming they will display enantiomorphism in the precisely opposite and complementary sense, the facial forms characteristic in this dextro-salt of the right termination of the digonal axis being absent on that side of the systematic symmetry plane but developed on the left side instead, and vice versa, and that the two enantiomorphous forms will together make up the whole of the faces required by the full symmetry of the monoclinic system.
A concrete instance like this, worked out practically in the laboratory, brings home the precise nature of this interesting relationship, between crystallographic and molecular enantiomorphism on the one hand and optical activity on the other hand, in a particularly clear and forcible manner. It is hoped that this brief account of it will also consequently have been of assistance to the reader, in more clearly appreciating the main points of this chapter.
CHAPTER XII
EFFECT OF THE SYMMETRY OF CRYSTALS ON THE PASSAGE OF LIGHT THROUGH THEM. QUARTZ, CALCITE, AND GYPSUM AS EXAMPLES.
The action of transparent crystals on the rays of light which they transmit is a subject not only of the deepest interest, but also of the utmost importance. For it is immediately possible to detect a cubic crystal, and to discriminate between two groups, optically uniaxial and biaxial respectively, of the other six systems of symmetry, three systems going to each group, by this means alone. For a cubic crystal is singly refractive in all directions. A 60°-prism, for instance, cut from a cube of rock-salt, for the purpose of obtaining the refractive index of the mineral by the ordinary method of producing a spectrum and arranging it for minimum deviation of the refracted rays, affords but a single spectrum, or a single sharp image of the spectrometer slit when the latter is fed by pure monochromatic light instead of ordinary white light. This is true however the prism may have been cut, as regards its orientation with respect to the natural crystal faces.
But a 60°-prism cut from a crystal belonging to the optically biaxial group, composed of the rhombic, monoclinic, and triclinic systems of symmetry, will always afford two images of the slit or two spectra, corresponding to two indices of refraction; and, when the orientation of the prism is arranged so that the refracting angle is bisected by a principal plane of the ellipsoid which represents the optical properties, and the refracting edge is parallel to one of the principal axes of the optical ellipsoid, the prism, when arranged for minimum deviation of the light rays, will at once afford two of the three refractive indices, α, β, γ, corresponding to light vibrations along two of the three principal axial directions of the ellipsoid. The two indices which the prism affords will be (1) the one which corresponds to vibrations parallel to the refracting edge, and (2) that which corresponds to undulations perpendicular to the edge and to the direction of transmission of the light through the prism (the third axis of the ellipsoid). For the vibrations of the light in the two rays into which the beam is divided on entering the crystal are both perpendicular to the direction of transmission and to each other; the two images or spectra produced owing to the double refraction, that is, owing to the different velocities of the two mutually rectangularly vibrating rays, thus correctly afford the means of determining two of the three principal (axial) refractive indices.
Gypsum, the monoclinic hydrated sulphate of lime, CaSO4.2H2O, already referred to in connection with the Mitscherlich experiment in Chapter VII., is an excellent substance to employ for the demonstration of this fact, by cutting and polishing a 60°-prism out of a clear transparent crystal of the mineral as above described; and if a Nicol prism be introduced in the path of the rays, one spectrum or monochromatic image will be extinguished when the Nicol is arranged at its 0° position, and the other when the Nicol is rotated 90° from this position. This proves that the two rays affording the two refractive indices are polarised in planes at right angles to each other, and, moreover, enables us to verify that the planes in which the vibrations of the two rays occur are actually parallel and perpendicular respectively to the refracting edge of the prism. For the two extinctions occur when the vibration plane of the Nicol is either vertical, parallel to the prism edge, or horizontal, perpendicular thereto.