ELLIPTIC POLARIZATION. 183 



and the preceding equation becomes 



y* + x* = a*. 



The path described by the molecule is then a circle. The 

 same thing is true, when a - /3 is any odd multiple of 90. 



(194) The nature of the elliptic polarization is completely 

 denned, when we know the direction of the axes of the ellipse, 

 and the ratio of their lengths. 



These may be determined experimentally. In fact, when 

 the elliptically-polarized ray is transmitted through a double- 

 refracting prism, whose principal section is parallel to one 

 of the axes of the ellipse, it is resolved into two plane-po- 

 larized rays, one of which has the greatest possible intensity, 

 and the other the least. Accordingly, the direction of the 

 principal section, for which the two pencils are most unequal, 

 is the direction of one of the axes ; and the square roots of 

 the intensities are in the ratio of their lengths. 



The direction of the axes of the ellipse may be more con- 

 veniently determined by turning the prism until the two 

 pencils are of equal intensity : the principal section is then 

 inclined at an angle of 45 to each of the axes. 



(195) When a plane-polarized ray undergoes reflexion, 

 the reflected light is, generally, elliptically polarized. For a 

 plane-polarized ray may be resolved into two, polarized re- 

 spectively in the plane of incidence, and in the perpendicular 

 plane ; and we shall presently see that the effect of reflexion 

 is, in general, to alter the phases of these two portions, and 

 by a different amount. Hence the reflected light is com- 

 pounded of two plane-polarized rays, whose vibrations are at 

 right angles, and whose phases are no longer coincident ; it 

 is therefore elliptically polarized (193). 



The first case in which this effect was observed was that 

 of total reflexion. 



