Gem-Stones and Their Distinctive Characters

by George Frederick Herbert Smith

2. UNIAXIAL
(Circular Polarization)

3. BIAXIAL
(Crossed Brushes)

4. BIAXIAL
(Hyperbolic Brushes)

INTERFERENCE FIGURES

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 a faceted stone to find a pair of faces perpendicular to the required direction. Nevertheless, so long as a portion of the figures described is in the field of view, the character of the double refraction, whether uniaxial or biaxial, may readily be determined.

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 visible in the field move up or down the scale in general from or to maximum and minimum positions. The manner in which this movement takes place depends upon the character of the double refraction and the position of the facet under observation with regard to the optical symmetry of the stone. In the case of a uniaxial stone, if the facet be perpendicular to the crystallographic axis, i.e. the direction of single refraction, neither of the shadow-edges will move. If the facet be parallel to that direction, one shadow-edge will move up and coincide with the other, which remains invariable in position, and away from it to a second critical position; the latter gives the value of the extraordinary refractive index, and the invariable shadow-edge corresponds to the ordinary refractive index. This phenomenon is displayed by the table-facet of most tourmalines, because for reasons given above ([p. 11]) they are as a rule cut parallel to the crystallographic axis. In the case of facets in intermediate positions, the shadow-edge corresponding to the extraordinary refractive index moves, but not to coincidence with the invariable shadow-edge. The case of a biaxial stone is more complex. If the facet be perpendicular to one of the principal directions one shadow-edge remains invariable in position, corresponding to one of the principal refractive indices, whilst the other moves between the critical values corresponding to the remaining two of the principal refractive indices. In the interesting case in which the facet is parallel to the two directions of single refraction, the second shadow-edge moves across the one which is invariable in position. In intermediate positions of the facet both shadow-edges move, and give therefore critical values. Of the intermediate pair, i.e. the lower maximum and the higher minimum, one corresponds to the mean principal refractive index, and the other depends upon the relation of the facet to the optical symmetry. If it is desired to distinguish between them, observations must be made on a second facet; but for discriminative purposes such exactitude is unnecessary, since the least and the greatest refractive indices are all that are required.