MAGNETISM AND LIGHT 331 



for a ray in which the rotation is clockwise as seen from the source* 

 and the value 



for a ray with the opposite rotation. 



If the two frequencies are N r N 2 , then 



where v = 



As the natural frequencies for two circularly polarised rays with 

 opposite rotations thus differ, they have different velocities, v v u 2 , 

 given by 



1 yO 



= K+ ^, . 5 =K-r- 



-w (N 2 -n 2 ) 



=K-4- 

 2 " r 



(3) 



If we Mibtnict the first of these from the second we get 



1 JL- *P M 



v* v* (N 2 -n 2 ) 2 



a result which is due to Voigt. 



We have taken v as positive for negative elections, and as 



yu 1 , which is proportional to -3, usually increases as we approach an 



absorption band from the long wave side, we may take ft as usually 

 positive. Hence (4) is usually positive, or v^> r a and a circularly 

 polarised ray in which the rotation as seen from the source is 

 clockwise moves with greater velocity than a ray with counter- 

 clockwise rotation. The rotation therefore has the same sign 

 whetluT n \^ li-vi than or greater than N. 



If a ray of plane-polarised light is resolved into two co-existing 

 circular components, and we assume that they have different 

 velocities as given by (3), the clockwise component moves the faster 

 and the plane of polarisation rotates clockwise or in the direction 

 of the current round the ray which would produce the field in which 

 it is travelling. 



If v l and r 2 are nearly equal, we may put the rotation pel 

 unit length (p. 328), by aid of (4), in the form 



