124 On the Laws of Crystalline 



a fluid medium whose index of refraction out of vacuo is repre- 

 sented by N, and let B and A respectively denote the ordinary 

 and the principal extraordinary indices of refraction out of vacuo 



N N 



into the crystal. Then putting -j- for a, and -=- for b, in the pre- 



A Jj 



ceding formula, and making 



Z 2 = ^ 2 sin 2 A + 2 cos 2 A, 

 we readily deduce 



A*&-I?N* 



tan ' CTi=2 - 



Hence we perceive that if L~ = AB, that is, if 



tan A = v/ 

 A 



(in which case A will never be much above or below 45), the 

 value of OTI will be always possible ; for then we shall have 



(70) 



But if A be different from this, and of course U not equal to 

 A B, the value of t^ may become impossible for certain values 

 of N. For it is clear that if JV lie between the limits L and 



AB 



-f-, the numerator and denominator of the fraction (69) will 

 _/> 



have unlike signs, and the tangent of sjj will be the square root 

 of a negative quantity. In this case, therefore, if common light 

 be incident, it will " refuse to be polarized," as Brewster ex- 

 presses it ; in other words, it will be impossible to find an angle 

 of incidence at which the reflected pencil will cease to contain 

 light polarized perpendicularly to the plane of incidence, or at 

 which the reflected transversal r' 3 will vanish. With all values 

 of 2V, except those which are included between the narrow limits 



AB 



L and =-, the polarizing angle is possible. It is zero at the 

 Li 



latter limit, and 90 at the former. Outside these limits it 



