Refraction for Electric Wares, 195 



Solving, 



l_cos 2 = A 2 cos 2 0-2ABcos0 + B 2 ; 



(A 2 + 1) cos 2 0-2AB cos 0=1 -B 2 ; 



2* 2 ^ B a± A2B2 - 1-B' J , A 2 B 2 



A 2 -B 2 + l 



~ (A 2 + l)* ; 

 AB 1 



cos 



"=Sqa±l?+iV A '- B ' +I - 



As a step toward a more general treatment of this equation, 

 let us investigate the case where 



then 



We should have 





A= 

 B = 



X 



2tt 



1 

 (« + *)' 



X 



ft. a 



27T (a-f^J 2 * 



Whence it is seen that in our iparticular problem where 

 X = 4'4, and a = 18, 



/4'4\ 2 1 



A2 is less than im) (w 



(18/ 



which is negligible in comparison with unity. B 2 is less than 

 A 2 and is also negligible in comparison with unity, 



.-. cos0 = AB + l. 



But AB is less than A 2 and may be neglected in com- 

 parison with unity ; 



.*. cos#=+l, 



2ttx 



n\ 



where n is any integer. 



