Form of Newton's Rings. 

 Fig. 3. 



K 



227 



We shall also write 



z 1 cos 6= (S 2 — $i) sin 2 6 = d 



fJ? COS 3 #! 



cos 6 sin 2 6 ; 



1 fju cos ^ ^ cos 6 X 



• (iv.) 



With the assistance of this change of symbols, we shall con- 

 sider the retardations of systems of incident rays slightly in- 

 clined to the incident rays hitherto considered. 



If <f> be the angle between such rays ((f) being small) and 

 -\{r the angle which the plane through the two rays makes with 

 the plane xz 9 we have 



I = sin 6 — cos 6 . <f> cos yjr, 



m= (f> sin yjr y 



n = cos 6 -f sin 6 . <£ cos yjr. 



fjb 2 n^ = fjb 2 — l + n 2 =//, 2 cos 2 1 + 2 sin 6 cos 6 . </> cos -^ + . . 



1 1 [~i sm cos ^ i . "1 



^nj /x cos a 1 L /ir cos 2 ^ r r J 



• (v.) 





