Phase Difference resulting from Metallic Reflexion. 475 

 But 



r — r„ . or r 01 



r approx. an 



d sin — ~ = sin^- — -rf 



pprox. Emu sin — -- - = sm-^ 



2 " rr " 2 

 Therefore sini — sin i P = /acqs r Sr p (4) 



But from (3) 



\ 



Jjjit sin 



Sr v = „-£ 



substituting in (4) for 8r p we get 



. . . . a cos rpX 

 sin 2 — sm i« = ™ h — 



Zfjbt sm r 



2ftanr' 



Expanding 



2 cos —t-^ sin -^r^ = n ,;— = lv/j 

 2 2 2£tanr 7 



where K = 



l'£ tan r 



Let i — ip — Q VJ so that i p = i — i 



and i + ip _ . 6 V 



~2~' "■*■"?■' 



and . i— L . 0» 0« 



sin — ~-^ = sin :? = .- . 



We get /. 6p\ Kj 



cos ' • 



h ' P 



(<-*)-? <=' 



Now P can be found by observation of the distance of 

 the pih band from the zero band and dividing it by the 

 focal length of the camera lens. Substituting in equation 

 (5) gives us the value of i, since k is readily evaluated from 

 the known constants. By taking every value of p from 1 

 upwards, the corresponding value of i is deduced and the 

 mean value of i found out. Values of i for the successive 

 bands can then be found out by calculation from the relation 



sin i p = sin i — Kp (6) 



After this preliminary consideration of the elementary 

 theory applicable to the present case, we proceed as follows 

 to apply it to the case of metallic reflexion. When simple 

 multiple reflexion takes place in a parallel plate of glass 

 bounded by air, we have the simple relation 



2yui cos r = nX. 



