If a single spectrum be afforded, which remains single on rotation of the Nicol, the prism is of glass or of a uniaxial crystal cut so that the light passes along the optic axis. If two spectra be shown when the Nicol is arranged in the neighbourhood of its 45° position, the crystal is a doubly refracting one, and if orientated so that the single optic axis, if the crystal be uniaxial, is parallel to the refracting edge, or, if the crystal be biaxial, so that the refracting edge is parallel to one of the three principal axes of the optical ellipsoid and its bisecting plane is parallel not only to this but also to a second principal axis, then one spectrum, corresponding to one principal refractive index, will extinguish when the Nicol is rotated to its 0° position, and the other spectrum, corresponding to a second principal refractive index, will be quenched on rotation of the Nicol to its 90° position.
The separation of the two spectra on the screen depends on the amount of the double refraction, and in the case of calcite this is exceptionally large, so that the two spectra are widely separated on the screen. They differ also considerably in dispersion. In the case of quartz the double refraction is very small, and the spectral images of the slit are consequently so close together as almost to touch one another. The pair of spectra afforded by gypsum are similarly very close together, owing also to weak double refraction. The amount of the double refraction is measured by the difference between the uniaxial indices ε and ω, or that between the minimum and maximum biaxial indices α and γ. The two spectra given by quartz and calcite will correspond to ε and ω, and the greatest separation of spectra occurs in the case of gypsum when the spectra are those corresponding to α and γ, and not to α and β or β and γ.
It will now be useful and very helpful to examine more closely into the nature of the beautiful mineral quartz, in order that a series of interesting experiments may be described with it, which will assist largely in rendering the optical characters of crystals clear to us.
Quartz, rock-crystal, although perhaps the commonest and best known of all crystallised substances, the naturally occurring dioxide of silicon SiO2, is yet one of the most remarkable and fascinatingly interesting. To begin with, as explained in the last chapter, quartz belongs to one of the eleven enantiomorphous classes of lower than full systematic symmetry, those which exhibit two mirror-image forms related to one another like a pair of gloves. The particular class of the eleven to which quartz belongs is the trapezohedral class of the trigonal system, and two typical left-handed and right-handed crystals are shown in Fig. 68 and Fig. 69 respectively.
There is one principal form which is common to both the hexagonal and trigonal systems, namely, the hexagonal prism, and this is the chief form exhibited by quartz crystals. They are terminated by an apparently hexagonal pyramid, but which really consists of a pair of complementary rhombohedra, which are purely trigonal forms; three upper faces of each rhombohedron are developed at one end of the prism which may be regarded as the upper, and the three lower faces of each of the two individual rhombohedra likewise at the lower end of a fully developed doubly terminated crystal. The rhombohedron is the characteristic form of the trigonal system of crystal symmetry, the systematic crystallographic axes being parallel to its edges. It is like a cube deformed by extension or compression along a diagonal, which latter is arranged vertically, and becomes the trigonal axis of symmetry (not a crystallographic axis), as shown in Fig. 70.
Fig. 68.
Fig. 69.
Left-handed and Right-handed Crystals of Quartz.
When two rhombohedra are equally developed, one being rotated with respect to the other 60° round the vertical trigonal axis of symmetry, they together resemble a hexagonal pyramid, and crystals of quartz thus terminated at both ends are not uncommon, so that at first sight a quartz crystal might be mistaken for a hexagonal prism doubly terminated by the hexagonal pyramid, and the mineral considered, in error, to belong to the hexagonal system.