Gem-Stones and Their Distinctive Characters

by George Frederick Herbert Smith

Fig. 14.—Refraction across a Plane Surface.

We see, then, that when light falls on the boundary of two different media, some is reflected in the first and some is refracted into the second medium. The relative amounts of light reflected and refracted depend on the angle of incidence and the refractive indices of the media. We shall return to this point when we come to consider the lustre of stones.

We will proceed to consider the course of rays at different angles of incidence when light passes out from a medium into one less dense—for instance, from water into air. Corresponding to light with a small angle of incidence such as I₁O (Fig. 15), some of it is reflected in the direction OI´₁ and the remainder is refracted out in the direction OR₁. Similarly, for the ray I₂O some is reflected along OI´₂ and some refracted along OR₂. Since, in the case we have taken, the angle of refraction is greater than the angle of incidence, the refracted ray corresponding to some incident, ray I_cO will graze the bounding surface, and corresponding to a ray beyond it, such as I₃O, which has a still greater angle of incidence, there is no refracted ray, and all the light is wholly or totally reflected within the dense medium. The critical angle I_cON, which is called the angle of total-reflection, is very simply related to the refractive indices of the two media; for, since r is now a right angle, sin r = 1, and equation (a) becomes

n sin i = n´ (b)

Hence, if the angle of total-reflection is measured and one of the indices is known, the other can easily be calculated.

Fig. 15.—Total-Reflection.

The phenomenon of total-reflection may be appreciated if we hold a glass of water above our head, and view the light of a lamp on a table reflected from the under surface of the water. This reflection is incomparably more brilliant than that given by the upper surface.

The refractive index of air is taken as unity; strictly, it is that of a vacuum, but the difference is too small to be appreciated even in very delicate work. Every substance has different indices for light of different colour, and it is customary to take as the standard the yellow light of a sodium flame. This happens to be the colour to which our eyes are most sensitive, and a flame of this kind is easily prepared by volatilizing a little bicarbonate of soda in the flame of a bunsen burner. A survey of [Table III] at the end of the book shows clearly how valuable a measurement of the refractive index is for determining the species to which a cut stone belongs. The values found for different specimens of the species do in cases vary considerably owing to the great latitude possible in the chemical constitution due to the isomorphous replacement of one element by another. Some variation in the index may even occur in different directions within the same stone; it results from the remarkable property of splitting up a beam of light into two beams, which is possessed by many crystallized substances. This forms the subject of a later chapter.