476 Interferometer Method of determining Phase Difference. 



But, for the case of light reflected from one of the surfaces 

 covered by metal and polarized in the plane of incidence, 

 this becomes 



Q 



2 fit cos (r + Br) 4- ~- X = nX . ... (7) 



when we account for the displaced band as being due to a 



change of phase on metallic reflexion. When the band shifts 



to its new position as a result of the phase difference, the 



change in the angle of incidence corresponds to the term Br 



and the phase difference ot ' is taken into consideration by 

 n 



the term k~X. 



Expanding (7), 



a 



2 fit cos r cos Br— 2 fit sin r sin Br -\- —~ X — nX, 



i. e. 2 fit cos r — 2 fit sin rBr + ~— X = nX, 





 i. e. n\ — 2iit sin r Br + ^- X = ?iX, 



i. e. 2 fit sin r Br = — \, 



and therefore 



0=—2fdamrSr. ... (8) 



But sirit = /xsinr. 



Differentiating cos t Bl = fi cos r Br. 



cos iBi 

 Therefore Sr = ^^. 



Substituting for Sr in (8) 



- 2tt /0 , . .cosihi 



= — ( 2 at sin ?■) 



X fiQosr 



= - £ tan r cos i Bi 

 X 



= K.' cos iBi, W 



4<7T 



where K = — — t tan 



A, 



In practice, with the constant K' evaluated from the known 

 constants of the plate, to evaluate 6 the phase difference, the 

 normal (glass-air) system of bands is measured out, and 

 getting by subtraction the distance of each from and 



