428 C. Travis — Behavior of Crystals in Light 



parallel to the axis. The area of the pointy is obviously zero 

 compared to the total area of the source, no matter how small 

 we may make the latter. 



It appears from this that interior conical refraction is a 

 purely mathematical ideal, never attained in practice. Yet it 

 is a well-known fact that a small source of light (a pin hole), 

 viewed along the optic axis of a biaxial crystal, appears not 

 as a double image, but as a luminous ring. Voigt* has shown 

 that what is observed in this case is not interior conical refrac- 

 tion, but simply an approximation to it. His reasoning may 

 be summarized as follows : 



A hollow cone of rays, of very small angular radius a, and 

 surrounding the axis, traverses the crystal in two hollow cones 



of radius, —*- ± a, where <£j is the angle of the cone of interior 



refraction. A solid cone of rays, of the same angular radius, 

 will traverse the crystal under the same conditions in the 

 annular space included between the two cones of radius 



— ± a. If, however, we consider not the summation of the 



effects produced upon a cone of rays, but the effect upon any 

 individual ray, we see that this ray undergoes simple double 

 refraction, and traverses the crystal in two definite rays. In 

 other words, there is no essential difference between the 

 behavior of rays near the axis and that of those at an appreci- 

 able distance from it. 



§2. Plane polarized light is split up, by passage through a 

 biaxial crystal, into two sets of rays, vibrating at right angles. 

 The components of these vibrations, in any one plane (obtained 

 by placing the analyzing nicol above the crystal), produce 

 certain definite interference effects. From the foregoing, light 

 in the neighborhood of the optic axis forms no exception to 

 this ; but as the divergence of the two complementary rays is 

 often a maximum near the optic axis, it is well to consider the 

 effect produced by having the source of light at a finite dis- 

 tance from the section. 



A ray SA (figure 1), from a source S, is divided, upon 

 entering the crystal, into the rays AB and AC, which vibrate 

 at right angles. From the same source, another ray, SD, may 

 be found, which will divide into DC and DE ; C is then the 

 common point of emergence of one ray from each of the points 

 A and D. These rays are polarized at right angles. If the 

 crystal is between crossed nicols, interference takes place 

 between the components of AC and AD, parallel to the plane 

 of the upper nicol. The effect produced is dependent upon 



*Voigt, W., Ann. Phys., xviii, 1905, p. 645. 



