414 Eioell — Gibos' Geometrical Presentation of the 

 Vertical lines are imaginary. In fig. 2, let i:j = 15 = — - 



16 = A 2 . Since — = A 2 + C 2 , 63 =CA 65 = C„ 2 . Let 62 be a mean 

 y 2 



proportional between 63 and 65. Then 62 = C,C 2 , 64 = — 62 



and we have the simple formulae : 



_ CV-CA 32 R P _ 14 

 E C^ + CA 34 ' R 5 ~" 12 



To apply these expressions to any case of reflection, take 



— as unity, and lay off sin *i as (A 2 , Tej) ; cos s i as C, 2 , (63) ; 



1 In 2 . . . \ 



and 15 as — ^ l^, where n is the refractive index). Locate 



v -i \ n i / 



62 and 64, the mean proportional, and find the above ratios. 

 Fig. 2 is thus drawn for light, incident in air, at 48°, upon 

 glass of refractive index L53. 



5e = = = - • 237, R s = ' = - . 3.34. 

 R s 12 " 34 



Both are negative, i. e., there is a difference of phase of it 

 between R p and R s , and between R s and the perpendicular 

 component in the incident light. 



As the angle of incidence increases, 6 moves to the right and 

 therefore li decreases until, at the Polarizing Angle, it becomes 



R P 



zero and hence also ^- = 0. JS T ear grazing incidence A and 



R, CO 



hence 16 is large, =j^ is now positive and both it and R= are 



increasing with increasing angle of incidence. 



Suppose the light is passing in the opposite direction, i. e., 

 from a medium where the velocity is less to one where the 



3 

 . -CC, -* CQ 



■ - -C 



* dV«si — x- - - -cWo — •> 



n r^ 3 F 



<- 



u 



velocity is greater. The various quantities for small angles of 



32 . 



incidence are represented in fig. S. R s = — is positive, 



34 



_ L — — is negative and as the angle of incidence is increased, 

 R s 12 



