[ 345 ] 



XXXVIII. On Achromatic Polarization and Differential 

 Double Refraction. By D. B. Bkace, Ph.D., Professor of 

 Physics, University of Nebraska *. 



IF a ray of light polarized at 45° to the principal axes of 

 a crystalline plate pass normally through it, the relative 

 retardation of the components will be proportional to the 

 thickness and to the difference in the refractive indices. In 

 most crystals the differential double refraction in the visible 

 spectrum is normal, and the relative retardation increases with 

 the frequency, depending on the crystal. By crossing several 

 such plates the difference in the resultant retardation for ad- 

 jacent parts of the spectrum might be made a minimum. 



The object of this investigation was to determine whether 

 such minima existed, and what orders would give the best 

 results. Of the crystals examined, namely, Iceland spar, 

 quartz, selenite, mica, and aragonite, all wore found to give 

 more or less perfect achromatism through the greater part of 

 the visible spectrum. 



If di, e l5 &>!, d 2 , e 2 , <o 2 , . . . . are the lengths of the path and 

 the reciprocals of the velocities of the component rays in the 

 successive plates, and X the wave-length in vacuo, the relative 

 retardation or order N is given by the equation 



7 e x — w, e 2 — cy 2 e 3 — w 3 ^ 



where 



Hence 



Nx + ^ + N.^.^N; (la) 



N —J €l ~ c ° l N — J <?2 ~" &)2 



K*^*^--)-"- '- • (2) 



or 



$ (N 1 + N 2 + ....)=^ = 0;. . . . (2a) 



i. e. the difference in the relative retardation for two frequencies 

 will be a very small quantity if the equation holds. If it can 

 be satisfied throughout the visible spectrum, perfect achro- 

 matism will be possible. 



* Communicated bv the Author. 



