Reflection and Refraction of Light. 171 



Next consider the case in which the incident vibrations are 

 in the plane of incidence. 



Then C = 0, and from equation (14) 



.,_V a + a 2 ' , 

 and hence 



c, xjk? aA ' v ^ 



W-^') * (a + a 3 ')V 1+ £ (a+a,')V 2 



Ao Ai 



^2 



7 aA V — 1 



Vx 



r- 1 (a + a s ')Ui + ^ (a + a^Ug 



A 2 A^ 



Whence 



C,= V-l 



sin zi sm -^ — 



1 _ .A, 



D ["sinM^ + R)- sin 2 '-^- 2 ] 



D' sin (i + R) sin (i -R) + D sin 2 ^y^ 



A,= . A ; 



Drsin 2 ( ? ' + E)-sin 2 '-^ 2 



or, to the same degree of approximation as in the former case, 



. r Y —r 2 



< sm 2~ 



C,= V-l sm 2z |- cog( ._ R) +Msin ( i ._ R) ^/ZT] sin 2 (^ + K) * A ' 



A _ cos (z + E) — M sin (i + B) V^l sin (z— B) . 

 '""cos(i-E)+Msin(i— R) V^l 'sin(t + R) ' 



Hence the reflected ray will be in general elliptically 

 polarized, the component of the vibration in the plane of 

 incidence being practically the same as if the refracting 

 medium had no rotating power, the component of the vibration 

 perpendicular to the plane of incidence being extremely small. 

 At the polarizing angle for which R + z'=7r/2, the reflected 

 vibration is plane-polarized, and the vibrations will be at an 



N2 



