150 ON THE LIGHT REFLECTED 



Substituting 1 - sin 2 ^ for cos a, the expression for the intensity 



becomes 



(u + # 2 ) 2 - 4ww 2 sin 2 ~ 



(1 + ww 2 ) 2 - 4w* 2 sin 2 



When the media are the same on the two sides of the plate, 

 2 = - u, and the foregoing formula is reduced to the known 



one, 



4w 2 sin 2 I 

 1 = 



- w 2 ) 2 + 4w 2 sin 2 ^ 



The greatest and least values of I, in the general formula, cor- 

 respond to sin a = 0, or a = mir. When a = 2mir, the expression is 



reduced to 



\1 + uuz 

 When a = (2m + 1) TT, it becomes 



/ 



/ u - u 2 V 



\i - wJ * 



When u and t* 2 have the same sign, the former value is a maximum,. 

 and the latter a minimum ; the rings consequently begin from a 

 bright centre. On the other hand, when u and 2 have opposite 

 signs, the former value is a minimum, and the latter a maximum ; 

 and the rings begin from a dark centre. 



When the incident light is polarized in the plane of incidence? 

 the signs of u and w 2 are determined solely by the relative refrac- 

 tive densities of the plate, and of the two media which border it 

 on either side. When the refractive density of the plate is greater 

 or less than those of both media, M and u z are of opposite signs, and 

 the rings are dark-centred. On the other hand, when the refractive 

 density of the plate is intermediate to those of the two media on 

 either side, u and u z have the same sign, and the rings ar& 

 bright-centred. This inversion of the phenomenon was observed by 

 Young. 



