ROTATORY POLARIZATION 241 



crystal ; ^ and // the corresponding refractive indices ; 

 then 



But, if 9 be the thickness of the crystal, and S the interval of 

 retardation of the two waves after traversing it, the second 

 member of the preceding equation is obviously equal to 



$ 



g ^ or to 1 + - r 8 being very small in comparison to 0. 



We have therefore 



Now the angle of rotation is proportional to the interval of 

 retardation of the two circularly-polarized pencils ; and when 

 that interval is equal to the length of a wave in vacuo, the 

 angle of rotation is 180. Hence the interval of retardation 

 of the emergent rays corresponding to any angle of rotation, 



/o, will be X r-- , X denoting the length of the wave ; and the 



corresponding interval within the crystal is equal to the same 

 quantity, multiplied by the velocity of propagation, or di- 

 vided by the refractive index. Hence, if p be the rotation 

 corresponding to the thickness of the crystal, 0, we have 



and substituting this value in the preceding formula, 



,_ X P 



^ P 180 



it 



