246 Lord Rayleigh on the Reflexion of Light 



where 



<o = lx + my+nz—Yt 9 (22) 



and &=27r-r-wave length. In accordance with (2) we must 

 have 



lk + m/i, + nv = 0, (23) 



signifying that the electric displacement is in the plane of 

 the wave-front. If we now write 



n=n</* w , 



and substitute the values of/, g, h from (21) in (19) we find 



X(Y 2 -a 1 2 ) = ik- i n o . I, &c, 

 so that by (23) 



I 2 , m 2 n 2 _ (9V 



v 2 -v v 2 -<v ^v 2 -^ 8 " ' " ' ' "• [ ) 



which is Fresnel's law of velocities, leading to the wave-sur- 

 face discovered by him. 



Reflexion at a Twin Plane. 



We are now prepared for the consideration of our special 

 problem, viz., the reflexion of plane waves at a twin surface 

 of a crystal. We suppose that the plane of separation is x= 0, 

 and we assume that there is a plane perpendicular to this 

 (z = 0), with respect to which each twin is symmetrical. The 

 only difference between the two media is that which corre- 

 sponds to a rotation through 180° about the axis of x 9 per- 

 pendicular to the twin plane. 



In consequence of the symmetry the axis of z is a principal 

 axis in both media ; but the axes of x and y are not principal 

 axes. For the relation between force and strain in the first 

 medium we may take 



P=4tt(A/+B#), Q=4tt(B/+C^), E=4ttDA. . (25) 



In the second medium we may in the first instance assume 

 similar expressions with accented letters ; but the peculiar 

 relation between the two media demands that A' = A, C'=C, 

 D' = D, B'= — B. Thus for the second twin medium, 



P = 47r(A/-B<7), Q = 47r(-B/+C#), E=4ttDA, . (26) 



the only difference being the change in the sign of B. If B 

 vanish, all optical distinction between the twins disappears, 

 and there can be no reflexion. The magnitude of B depends 

 upon the intensity of the double refraction in the twins, and 

 also upon the angles between the principal axes and the twin 



