366 F. E. Wright — Measurement of .Extinction Angles. 



thickness <# n includes with the principal plane of the polarizer 

 and a , the angle between 7^ of the inserted plate or wedge of 

 thickness d^ and the polarizer plane, the relative intensity is 

 given by the formula, and d^y^ — a^ ) ■—• T, and djy' — aj) 

 = T„ then 



1 1 = sin 2(0 2 -0 x ) sin 20, cos 20 2 sin ^ T a 



T 



9. 



+ sin 2(0 a — 0J cos 20 2 sin 20 2 sin -^ T 2 



+ cos 2 (0. 2 -^) sin 20, sin 2(9 2 sin ~ ( T i~ P 2 ) 



- sin 2 (0 2 -0J sin 20 x sin 20 2 sin 2 ^(T : -T 2 ) 



From this formula the relative intensity can be calculated for 

 any given values of (0 V 2 ) and T 1 and T 2 . 



In case the crystal plate is of such a thickness that 



2-7T 



sin -=■ T 2 ==• 1 and at the same time the inserted plate is also 



9 TT T 



of a thickness that sin — ^~ == 1, this equation reduces to 



I, - sin 2 2(0,-00 

 an expression for a curve similar in every respect to those of 



fig. 2, but which is zero for 2 = 1 and also for # 2 = — + #, and 



readies its maximum of 1 at 2 = -- + #,. It can also be shown 



that for a given increment of # 2 as d0 2 , the ratio of the value 

 of the function for (0 2 + d0 2 ) to its value for # 2 -is greatest 

 when 2 is equal to #,. If, therefore, the angle 2 be so chosen 

 that the field is just illuminated, the change resulting from 

 small angles of 0, will be greater than for any other position 

 of the inserted plate. 



In the Calderon method described below, the calcite plates 

 are purposely so thick that they show the white interference 

 colors of higher orders in white light, in which case the thick- 

 ness is so great that for a number of different colors through- 

 out the spectrum the path difference of the emergent wayes is 

 a whole number of wave lengths, in other words, in the 

 Calderon method it is permissible for practical purposes to con- 

 sider the plate of such a thickness that for white light the 



expression sin 2 T T^ is unity, and that therefore the angle # 2 



A 



should be small in order to secure the best results, so small in 

 fact that the illumination of the field is just visible. 



