ELLIPTIC POLARIZATION. 185 



of the two portions of the reflected light amounted to one- 

 eighth* of an undulation, when the angle of incidence was 

 54 37 X . Polishing, therefore, a parallelepiped of this glass, 

 whose faces of incidence and emergence were inclined to the 

 other faces at these angles, 

 it followed that a ray 

 RR'R^R"', incident per- 

 pendicularly on one of 

 these sides, and once re- 

 flected at each of the others, at R' and R", would emerge 

 perpendicularly at the remaining side, the difference of phase 

 in the two portions of the twice-reflected ray amounting to a 

 quarter of an undulation. If, then, the incident ray be pola- 

 rized in a plane inclined at an angle of 45 to the plane of 

 reflexion, the emergent light will be circularly-polarized. 

 This was found to be the case on trial, and the theory 

 thereby verified. The parallelepiped described is well known 

 under the name of Fresnel's rhomb ; and is of essential 

 service in all experiments relating to circular and elliptic 

 polarization. 



If the circularly-polarized ray be made to undergo two 

 more total reflexions, in the same plane and at the same 

 angle, by transmitting it through a second rhomb placed 

 parallel to the first, it will emerge plane-polarized ; and its 

 plane of polarization will be inclined 45 on the other side of 

 the plane of reflexion. In fact, the two additional reflexions 

 increase the difference of phase of the two portions, into which 

 the light was originally resolved, from 90 to 180 ; and we 

 know that two equal vibrations, whose phases differ by 180, 

 compound a single right-lined vibration, whose direction 



* In order to produce a difference of phase of ajjuarter of an undulation by 

 a single reflexion, the refractive index should bey 



^ . , 



