268 ADAMS: RAYLEIGH-ZEISS INTERFEROMETER 



In the initial position (angle of incidence = 45°) d = 0°, and 

 therefore 



(2) n = if-;^(Vi7-l) 



Hence, the optical path difference p resulting from the tilt- 

 ing of the plate through an angle d is . 



'3) P-Po-P-^^ 



Vh - 1 - VH + sm2e + cosd-\-mid\ 



This formula may be applied in a number of ways. For a 

 compensator plate of given thickness and refractive index one 

 can calculate the sensitiveness of the instrument by differentiat- 

 ing with respect to 9; moreover its range for given values of 6 

 may be readily computed. • 



It is interesting to note the relation between sensitiveness and 

 refractive index of the plate. For 6=0° 



dp h / 1 \ 



The values of dp/d 6 for plates of unit thickness are shown below. 



sensitiveness 

 dp/dd 



0.34 

 0.44 

 0.51 

 0.54 



Inspection of this table shows the comparatively small influence 

 of refractive index on the sensitiveness of the compensator plate. 

 In a modified form it maj^ also be used to obtain a small cor- 

 rection to the reading (on the drum D of the micrometer screw) 

 such that the ''corrected reading" will be strictly proportional 

 to the refractive index difference {v) of the solutions or mixtures 

 under investigation. Thus if R is the travel in mm. of the 

 screw and a the length in mm. of the arm — that is the con- 

 stant perpendicular distance between the center of rotation and 



T> 



the line of motion of the screw — then 6 = tan —. Hence 



a 



