ADAMS : RAYLEIGH-ZEISS INTERFEROMETER 



267 



interposed glass plates (Pi, -P2, fig. 1); the amount of this tilting 

 is then a measure of the path-difference between the two sides 

 and hence of the difference in refractive index of the contents 

 of the pair of cells Ci, Co. The compensator plate is fastened 

 at an angle of about 45° to a movable arm parallel to the direction 

 of the light and is tilted by means of a micrometer screw which 

 bears against the arm and moves in a fixed direction perpendicu- 

 lar to the arm when in its zero-position (see fig. 2) . The optical 

 path-difference resulting from the 

 tilting of the plate through a certain 

 angle 9 may be calculated as follows : 

 Consider a certain path, of length 

 K, traversed by a beam of light, and 

 introduce into this path a plane- 

 parallel glass plate (fig. 3) . ' Let 45° 

 + 6 he the angle of incidence, h the 

 thickness of the plate, n its refrac- 

 tive index and no that of the surrounding medium (air) 

 may easily be shown that the air-path of the beam 



Fig. 3. Diagram to illustrate 

 path of light beam through com- 

 pensator plate. 



It 



ki + /v3 = K 



h 



V2 

 and that the glass-path 



COS d -f sin d -\- 



rioil - sin20j 



V2n^-nli\ -sin 2 5). 



V2 n h 



V2n'' -7il (1 -sin 2^) 

 Now the optical path-length P is by definition equal to 2 k n. 

 Accordingly, 



h 



P=''^^- V2 



V2 ^2 - rio (1 - sin 2 - no (cos 6 + sin 6) 



Ordinarily no — 1 is very small compared to n — 1 ; consequently 

 we may put no == 1 . Then if we write H -= 2n^ — 1 , we have 



(1) 



P ^ K - 



h 

 V2 



V H + sm2d - (cos d + sin d) 



