Parallel to an Optic Axis. 



429 



the difference in phase at C, and this is due to the difference 

 in the optical length of the paths SAC and SDC. 



Let us assume that the wave-front of the two rays is essen- 

 tially normal to the optic axis, so that the front velocity (not 



ray velocity) is the same for each, and is equal to — ; let M^N" be 



the direction of the wave-front in the crystal and ~WW that 

 outside the crystal ; also let S A be very large compared to AD. 

 In the crystal, the path difference is j3 . AD. sin MNN', AC 

 having the longer path. Outside the crystal, the path differ 



Fig. 



2. 





B C E 









' 1 



4 



* 



t 



1 



it 



A 





D 





ence is AD . sin M'N^N", SD having the larger path. But sin 

 H'N'N=£. sin MNN'; therefore SAC is optically equivalent 

 to SDC. 



If, then, S is at a great distance, the two rays at C will be 

 in phase ; their vibrations will give a resultant which is parallel 

 to the plane of the lower nicol, and this resultant will be ex- 

 tinguished by the upper nicol. 



In discussing the case in which the source is at a finite dis- 

 tance, the condition that the section be taken normal to the 

 axis is assumed temporarily. (Figure 2.) The maximum phase 

 difference is that between the two rays that lie in the plane of 

 the optic axes; in the figure, this plane is taken as the plane of 

 the paper. 



Let Av=the path difference, SD — S A. (AC and DC are 

 optically the same.) 

 D=the distance of the source, SA. 

 ^>i=the angle of the cone of interior conical refraction. 



