6"= ^~ ] 



252 Lord Rayleigh on the Reflexion of Light 



coexist, 



e ' = (~-7)$Z-i) {(i+-)*+-(i+*)e.}, • (52) 



(w-^-l) < Cl + *)». + (1 + *>>©*}• • (5 3 ) 



It will be observed that although the fronts of the two inci- 

 dent waves © 1? ® 2 are not parallel, they are the waves that 

 would be generated by the double refraction of a single wave 

 incident from an isotropic medium upon a face of the crystal 

 parallel to the twin plane. 



Doubly Refracting Poiver small. 



Thus far our equations are general. Bat the interpretation 

 will be very much facilitated if we introduce a supposition, 

 which does not deviate far from the reality of nature, viz. that 

 the doubly refracting energy is comparatively small. There 

 is no new limitation upon the direction of the principal axes 

 relatively to those of coordinates, but we assume that A, 0, D 

 are nearly equal, and that B is small. We may imagine the 

 two twin crystals to be bounded by faces parallel to the twin 

 face, and to be embedded in an isotropic medium of nearly 

 similar optical power. Under these circumstances p 1} p 2 ; 

 Vj, V 2 are nearly equal, so that approximately «■= 1, o-=//, 2 //"i; 

 and we may write (52), (53) in the form 



*' = i^S^ {Wa0i+M ^ i+ft)02 »' • • (54) 



^-^F^l^Oi+^i + S/^®^. . . (55) 



It should be remarked that the intensities of the waves repre- 

 sented by ©x &c. are not simply proportional to S { 2 , &c. 

 Referring to (39), (40), we see that the intensity of ® 1} 6' is 

 measured by (r*+p i + /i l r )(® 1 3 , Q' 2 ) ; and that of O,, 6" by 



Plate bounded by Surfaces parallel to Twin Plane, 



Let us now regard the waves ® 1} <y) 2 as due to the passage 

 into the crystal of waves from an isotropic medium, under 

 such conditions (of gradual transition, if necessary) that 

 there is no loss by reflexion. The interface is supposed to 

 be parallel to the twin reflecting plane, and the optical power 

 to be so nearly equal to that of the crystal that the refraction 

 is negligible. Then, if the vibration parallel to y (perpen- 



