190 ELLIPTIC POLARIZATION. 



placed parallel to one another, with their reflecting surfaces 

 opposed ; and their distance was adjusted by means of a 

 screw. A ray of light, incident upon one of the mirrors, 

 will, after reflexion, fall upon the other in the same plane, 

 and under the same angle. It will then return to the first, 

 its plane and angle of incidence being unaltered ; and will 

 thus undergo a series of similar reflexions between the 

 mirrors, the number of which depends on their distance, and 

 on the angle of incidence. 



Now the incident ray, polarized in any plane, may be 

 resolved into two, polarized respectively in the plane of inci- 

 dence, and in the perpendicular plane. The planes of 

 polarization of these two components are unchanged by re- 

 flexion : but their phases are altered, and that unequally ; 

 and the reflected light, composed of them, is therefore ellipti- 

 cally-polarized. 



"When there are several reflexions in the same plane, and 

 under the same angle, the two components undergo the same 

 modification of phase at each successive reflexion, and the 

 difference of phase produced is equal to that produced by a 

 single reflexion, multiplied by the number of reflexions. But 

 the resulting light will be plane-polarized, when the difference 

 of phase becomes a multiple of 1 80 : we have, therefore, only 

 to increase the number of reflexions at the same incidence* 

 until the light is plane-polarized, and the difference of phase 

 produced by a single reflexion will be known. For, if e 

 denote the difference of phase sought, ne will be that pro- 

 duced by n reflexions. And, when the resulting light is 

 plane-polarized, ne = WITT, m being any integer number ; con- 

 sequently 



mir 



= . 



n 



* In practice it is more convenient to producu this effect by increasing the 

 incidence, the number of reflexions remaining unchanged. 



