THE DETERMINATION OF REFRACTIVE INDEX 193 



The Refractive Index of Anisotropic Substances. Crys- 

 tals are either isotropic or anisotropic. In isotropic crystals 

 light rays are refracted to an equal degree, no matter in what 

 direction through the crystals the rays are sent, since the velocity 

 of transmission of light is the same in all directions through the 

 crystals, providing the crystals have not been subjected to 

 stresses or strains. In the determination of the refractive indices 

 of isotropic crystals, it is obvious that the same value will be 

 obtained in all directions through the crystals. In the case of 

 anisotropic crystals, however, the rate of transmission of light is 

 different in different directions through the crystals. In order 

 to better appreciate the influence of these properties upon the 

 refractive index, it is necessary to briefly consider a few funda- 

 mental facts. 



A ray of light, when passing obliquely from one medium into 

 another whose rate of transmission for light rays is different, 

 will be deflected from its original path according to the equation 



C1T1 / \f 



- = . , in which i is the angle formed by the incident ray 

 sin r V 



and the normal, r the angle formed by the refracted ray and the 

 normal, and V and V the velocities of the transmission of the 

 light in the two media. When the rays pass from a medium 

 having a higher rate of transmission into one of lesser rate the 

 deflection is toward the normal, but when passing from a medium 

 with a lesser rate into one of higher rate the bending is away from 

 the normal. In microscopic work the light rays are usually 

 passing from air into a denser medium. If in the above equation 

 we assign to the velocity of light in air the value of i, the equation 



' sin i i , , sin i . ,, r , , . , r 



becomes - = . , but - is the expression for the index of 

 sin r V sin r 



refraction, from which it appears that the refractive index is 

 inversely proportional to the velocity of the transmission of light 

 in the medium. Since in anisotropic crystals, the rate of trans- 

 mission of light rays differs according to the direction through 

 the crystal in which the rays are sent, it is obvious that the re- 

 fractive index of an anisotropic crystal cannot be expressed by a 

 single value and further, that of the several values given by a 



