Gem-Stones and Their Distinctive Characters

by George Frederick Herbert Smith

Fig. 21.—Shadow-edges given by a doubly refractive substance.

We have so far assumed that the substance which we are testing is simple and gives a single shadow-edge; but, as may be seen from Table V, many of the gem-stones are doubly refractive, and such will, in general, show in the field of the refractometer two distinct shadow-edges more or less widely separated. Suppose, for example, we study the effect produced by a peridot, which displays the phenomenon to a marked degree. If we revolve the stone so that the facet under observation remains parallel to the plane surface of the dense glass of the refractometer and in contact with it, we notice that both the shadow-edges in general move up or down the scale. In particular cases, depending upon the relation of the position of the facet selected to the crystalline symmetry, one or both of them may remain fixed, or one may even move across the other. But whatever facet of the stone be used for the test, and however variable be the movements of the shadow-edges, the highest and lowest readings obtainable remain the same; they are the principal indices of refraction, such as are stated in Table III at the end of the book, and their difference measures the maximum amount of double refraction possessed by the stone. The procedure is therefore simplicity itself; we have merely to revolve the stone on the instrument, usually through not more than a right angle, and note the greatest and least readings. It will be noticed that the shadow-edges cross the scale symmetrically in the critical and skewwise in intermediate positions. Fig. 21 represents the effect when the facet is such as to give simultaneously the two readings required. The shadow-edges a and b, which are coloured in white light, correspond to the least and greatest respectively of the principal refractive indices, while the third shadow-edge, which is very faint, corresponds to the liquid used—methylene iodide. It is possible, as we shall see in a later chapter, to learn from the motion, if any, of the shadow-edges something as to the character of the double refraction. Since, however, each shadow-edge is spectral in white light, they will not be distinctly separate unless the double refraction exceeds the relative dispersion. Topaz, for instance, appears in white light to yield only a single shadow-edge, and may thus easily be distinguished from tourmaline, in which the double refraction is large enough for the separation of the two shadow-edges to be clearly discerned. In sodium light, however, no difficulty is experienced in distinguishing both the shadow-edges given by substances with small amount of double refraction, such as chrysoberyl, quartz, and topaz, and a skilled observer may detect the separation in the extreme instances of apatite, idocrase, and beryl. The shadow-edge corresponding to the greater refractive index is always less distinct, because it lies in the bright portion of the field. If the stone or its facet be small, it must be moved on the plane surface of the dense glass until the greatest possible distinctness is imparted to the edge or edges. If it be moved towards the observer from the further end, a misty shadow appears to move down the scale until the correct position is reached, when the edges spring into view.

Any facet of a stone may be utilized so long as it is flat, but the table-facet is the most convenient, because it is usually the largest, and it is available even when the stone is mounted. That the stone need not be removed from its setting is one of the great advantages of this method. The smaller the stone the more difficult it is to manipulate; caution especially must be exercised that it be not tilted, not only because the shadow-edge would be shifted from its true position and an erroneous value of the refractive index obtained, but also because a corner or edge of the stone would inevitably scratch the glass of the instrument, which is far softer than the hard gem-stones. Methylene iodide will in time attack and stain the glass, and must therefore be wiped off the instrument immediately after use.

(2) The Method of Minimum Deviation

If the stone be too highly refractive for a measurement of its refractive index to be possible with the refractometer just described, and it is desired to determine this constant, recourse must be had to the prismatic method, for which purpose an instrument known as a goniometer[3] is required. Two angles must be measured; one the interior angle included between a suitable pair of facets, and the other the minimum amount of the deviation produced by the pair upon a beam of light traversing them.

Fig. 22.—Path at Minimum Deviation of a Ray
traversing a Prism formed of two Facets of a
Cut Stone.

Fig. 22 represents a section of a step-cut stone perpendicular to a series of facets with parallel edges; t is the table, and a, b, c, are facets on the culet side. The path of light traversing the prism formed by the pair of facets, t and b, is indicated. Suppose that A is the interior angle of the prism, i the angle of incidence of light at the first facet and i´ the angle of emergence at the second facet, and r and r´ the angles inside the stone at the two facets respectively. Then at the first facet light has been bent through an angle i - r, and again at the second facet through an angle i´ - r´; the angle of deviation, D, is therefore given by

D = i + i´ - (r + r´).