32 On the Action of the Second Surfaces of 



When the pencil R A is incident on the first surface at the polari- 

 zing angle or 56° 45', the rotation produced by refraction at A is 

 about 2°, or the inclination I=45° + 2°:=47°; butthe maximum ac- 

 tion of the polarizing force at C is sufficient to make 1=0° whether 

 X is 45° or 47°. Hence C B is completely polarized in the plane 

 of reflexion, and the refractive action at b is incapable of changing 

 the polarization when 1 = 0°: the reason is therefore obvious why 

 the two rotations at A and b, of 2° each, produce no effect at the 

 maximum polarizing angle. 



If we now call 



9 =IncIination to the plane of reflexion produced by the 1st re- 

 fraction at A, 



cp' ^Inclination produced by the reflexion at C, 



(p"= Inclination produced by the 2nd refraction at 6, 



We shall have 



Cot (B= cos (i — i^) ; or tan (p = — —7^ -^vT 

 ^ V /? Y cos [i—i') 



. /cos (i-\-i') cos (i-\-i^) 



Tan (p''=tan a;l 7-. — v\=7 r- — vTTT 



^ \cos(t— t') (cos (i — i') )^ 



(cos (i — i') ) ^ 



Cot9''=cota; (cos (i-t') ) = ^ >• ■ vx 



^ \ \ /y cos(i4-*) 



These formulae are suited to common light where a; =45°, but when 



X varies they become 



Cot 9= cot X (cos {i—i') ) 



/ cos {i-\-i') 

 Tan 9' =^tan x 



-(cos {i—i')) 



/(cos {i — i') )^\ 



Cot 9''= (cot a; I /• , VN — /" 



^ ^ \ cos (»+* ) / 



■n ■ n • I • i^^^ (* ~ *')) 



Resuming the formula for common light, viz. cot 9"= f\-/\ ? 



COS [1 ~y~ 1 J 



it is obvious that when (cos {i — i'))^ = cos {i-\-i'), cot 9''=:!, 

 and 9"'=45°; that is, the light is restored to common light. 



In glass where to= 1.525 this effect takes place at 78° 7'; a little 

 below 78° in diamond ; and a little above 80° in water. 



At an angle below this, 9 becomes less than 45°, and ^the pencil 

 contains light polarized in the plane of reflexion -, while at all great- 

 er angles 9 is above 45, and the pencil contains light polarized per- 

 pendicular to the plane of reflexion. Hence we obtain the folbw- 

 mg curious law. 



