by Reflection from the Pole of a Magnet. 



331 



C COS a COS 27T-> 

 T 



c sin a cos 27r - •> 



T 



or, more briefly, 



a cos and a' cos 0, 



where is proportional to t. Let 

 Y be perpendicular to X and to 

 the reflected ray ; then, to obtain 

 the components x and y of the re- 

 flected vibration in the directions OX and OY, we must 

 apply to the preceding components the known laws of metallic 

 reflection. We find thus 



D Y 



x = ha cos 6, \ 



(i) 



y = ka f cos (O — cj)), 



where h and k are constants characteristic of the reflecting 

 metal. As the angle of incidence is about 75°, and therefore 

 very near the principal incidence, we may put 



. *=** • (2) 



Substituting in (1), and representing the amplitudes by b and 

 V) we find 



x— bcosd, \ ,„< 



y=-V sine J ' ' ^ } 



From these equations or otherwise we see that the reflected 

 vibration is elliptic, and that its principal rectangular compo- 

 nents are perpendicular and parallel respectively to the plane 

 of incidence. We see also that the elliptic polarization is left- 

 handed in the case of operation R, and right-handed in the case 

 ofL. 



Hence a simple method of compensating the effect of the 

 operation R, or of the rotation a of the incident vibration. 



7T 



Introduce a difference of phase — between the components x 



and y by means of a quarter-wave plate, and then turn the 

 second Mcol in the proper direction through a small angle 

 which is definitely related to a. This method I have not had 

 an opportunity of trying. 



To find another method. Let the elliptic vibration (3) be 

 represented by its rectangular components x' and y f , in direc- 



