Reflexion and Refraction. 125 



changes rapidly at first, until N has passed either of them by 

 a quantity considerable in proportion to the interval between 

 them. 



From (68) we find w^A, when = 1, or N-A\ and also 

 W! = 90-A, when 5 = 1, or N=B. In the latter case it is re- 

 markable that no light is reflected when common light is inci- 

 dent at the angle 90 -A. For then we have r' 3 =0; and because 

 *i = <2, we have likewise r 3 = 0. Therefore no light can enter the 

 reflected pencil. But this case deserves that we should consider 

 it more at large, without restricting ourselves to the supposition 

 that the axis of the crystal lies in the plane of incidence. 



Assuming then that N=B, or that the refractive index of 

 the fluid, which covers the reflecting surface, is equal to the 

 ordinary index of the crystal itself, we may observe that, in 

 this case, every angle of incidence, in every azimuth, has a 

 right to be regarded as a polarizing angle. In fact, common 

 light cannot suffer reflexion at the separating surface of the 

 crystal and the fluid, without becoming completely polarized. 

 For if polarized light be incident, and if r 3 and r' 3 be the uni- 

 radial reflected transversals, respectively belonging to the ordi- 

 nary and to the extraordinary ray, the former transversal must 

 necessarily vanish, for the same reason that no reflexion can 

 take place at the separating surface of two ordinary media 

 whose refractive indices are equal; and thus the actual re- 

 flected transversal will always coincide in direction with / 3 , 

 whatever be the direction of the incident transversal. Conse- 

 quently, if common light be incident, the whole reflected pencil 

 will be polarized in a plane passing through r' 3 , and making 

 with the plane of incidence an angle 0' 3 determined by the 

 second of formulae (39). By putting t z = *i in that formula, 

 and employing the expression (44), we first obtain 



n , cos (/i + ' 2 ) cos 0' tan a/ + sin (i t + t' 2 ) 



tan V 3 = : TjTT- 7 



sin u tan w 



_ cos (ii + i' 2 ) tan (p - i' a ) + sin (^ + 1' 2 ) 

 sin 6T tan a/ 



