FresneVs Reflexion of Liglit Thtonj. 313 



first surface reflected at an incidence of 



-M(^)>-']te)V-']* 



and 1/nth of the refracted ray incident on second surface at 

 an incidence 



We shall see that the latter expression is simply the former 

 transferred from the incident to the refracted ray. Multi- 

 plying the numerator and denominator of the former ex- 

 pression in the surd by — (\/n — 1) 2 //^ 4 (\A+ !) 2 > we g et 



But yLt -1 sin i = sin r, therefore 



sm 



'=K(^D>0V[(^)',H' 



thus proving the proposition. 



When the incidpnt liglit is polarized in the plane of 

 incidence — the undulations being perpendicular to that plane 

 — the equation is 



Ifn = gin* (i-r)/ sin 2 (i + r) = 2 S' - 8) 2 /(> 2 S' + S) 2 . 



Let S' = xS, then l//i^( y C6 2 % -l) 2 /(/^ 2 X+ l) 2 , whence 



_ (v/Vtl) 2 vA+1 y^-1 



The application of the proper value of % in this case is not 

 so complex. The +% value has to be employed when /u,>l y 

 and the — % value when //,< 1. 



Also, when 1/nth the incident light is reflected at the 

 first surface of a refracting plate, then ljnth. of the refracted 

 ray is reflected at the posterior surface. This can be shown 

 in the same manner as for light vibrating in the plane o£ 

 incidence. 



The reflexion of common light is usually treated as if the 

 light were composed of two equal rays polarized in and per- 

 pendicular to the plane of incidence ; hence, 



1 _ l/sin 2 (z— r) tan 2 (i — r)\ 

 n~ 2 Vsin 2 (?' + ?•) tan 2 (/ + r) / 



