Parallel to an Optic Axis. 



431 



of collimation of the instrument, the point that represents this 

 direction will lie at a distance from the center of the figure 

 proportionate to sin a. The pencil of light that falls upon the 

 section consists of rajs having all directions within certain 

 limits ; if in any given pencil the maximum divergence between 

 rays is 2a, a circle drawn upon the interference figure, with 

 radius proportionate to sin a, will represent the limits of the 

 pencil. The average intensity of that portion of the figure 

 lying within the circle is obviously equal to the relative amount 

 of light transmitted by the section, when this is illuminated by 

 the pencil under consideration. 



The intensity at any point of the interference figure may be 

 found from the following equations :* 



I=sin 2 20.sin 2 7rA (1) 



AX=Fp sin 4> x sin <£ 2 ") 

 if— -L\ ' 



2 [ a 2 W ! 



; m 



AA=Fpsin 2 <j>, 



y (For biaxial crystals.) (2) 



y (For uniaxial crystals.) (3) 



Equation (1) gives the relative intensity I at any point of 

 the figure, in terms of the phase difference A between the two 

 sets of interfering rays projected in that point, and the angle 

 that the vibration planes of these rays make with the planes 

 of the nicols. In equations (2) and (3), which give us A, p is 

 the thickness of the section measured along the wave-front 

 normal of the rays, $> x and cf> 2 the angles that this normal 

 makes with the two optic axes in a biaxial crystal, and <j> the 

 angle that it makes with the single axis in a unaxial crystal. 

 In both cases F is a function of the principal indices of refrac- 

 tion ; if (y-a) for a biaxial crystal is equal to ± (®-e) for a 

 uniaxial one, F will not be very different in the two cases. 



Near the optic axis, (2) may be written 



Fo 



A = —*- . <k sin 2V 



A 



* Liebisch, Th., Grundriss der physikalischen Krystallographie, Leipzig, 

 1896, p. 273, 336, 375. The above forms for the equations are somewhat 

 different from those given by Liebisch. 



