38 GENERAL CHARACTERS OF PRECIOUS STONES 



When the angle of incidence is greater than ACD, the angle of refraction will be 

 greater than BCE. In Fig. 9, let A^C represent another ray of light in the same plane of 

 incidence, such that the angle of incidence J^CB is greater than ACD, then the 

 corresponding refracted ray is represented by CB^. It will be seen from the figure that 

 the angle of refraction B-^CE is greater than BCE, which is the angle of refraction 

 corresponding to the angle of incidence ACD. Similarly in every case the angle of 

 refraction varies with the angle of incidence, and this variation is governed by a definite 

 law, namely, the law of refraction. 



In the plane of incidence and with C as centre (Fig. 9), let a circle of any convenient 

 radius be drawn. Let the circle cut the incident rays AC and A^C at the points A and A^, 

 and the refracted rays BC and B^C at the points B and B^. From these points drop 

 perpendiculars, AG, A-fi^, BF, B-^F^ upon the normal DE. Then the ratio of the 

 perpendicular AG to the corresponding perpendicular BF is the same as the ratio A^G^ to 

 -BjFj, and will alwavs be constant for the same substance whatever may be the angle of 

 incidence. Hence, when light passes from air into any particular stone, the following 

 relation holds for all rays : 



AG _ A^ _ 



BF " B-^F-^ " ~ '^' 



where w is a constant for that particular substance, but is diiferent for different substances. 

 This constant n is known as the refractive co-efficient, the refractive index, or the index of 

 refraction of the substance. As just pointed out, the refractive index is independent of 

 the angle of incidence ; it has a certain definite value in all specimens of the same kind of 

 precious stone, and will be different in different stones. 



Since, in the passage of light from the air into a stone, the angle of incidence is always 

 greater than the angle of refraction, it is easily seen from Fig. 9 that the perpendiculars 

 J(? and A^G^ will always be greater than the perpendiculars BF and B^F^\, the index 

 of refraction of all precious stones is therefore, when compared with that of air, always 

 greater than unity. 



The index of refraction of a stone can be determined accurately to several places of 

 decimals by various methods. For the purpose of identifying precious stones, however, 

 such a degree of accuracy is unnecessary, and refi'active indices will be given here, as a rule, 

 to only two decimal places. The following values may be given as examples, that of air, of 

 course, being 1 : 



Water . 

 Fluor-spar 

 Spinel . 

 Garnet . 

 Diamond 



11 = 1-33 

 n - 1-44 

 n = 1-71 

 n = 1-77 

 n = 2-43 



In passing from air into any of these substances, the bending of the rays of light is 

 greater the greater the refractive index of the substance, and conversely. The value of the 

 refractive index is in many precious stones very high, but is far higher in diamond than in 

 any other gem. The values for other stones will be given under the special description of 

 each. In comparing two substances with different refractive indices, the one with the 

 higher refractive index is known as the '' optically denser" substance, while the other would 

 be described as the " optically rarer " ; thus precious stones are "optically denser" than 

 water or air. 



A ray of light in passing from air into a stone immersed in liquid will be twice bent ; 

 once at the surface of separation between the air and the liquid, and again at the surface of 



