REFLEXION AND REFRACTION OF POLARIZED LIGHT. 101 



cording to Fresnel, that the periods of vibration of the incident 

 and reflected waves, which had been assumed to coincide at the 

 reflecting surface, no longer coincide there when the reflexion is 

 total ; or, in other words, that the ray undergoes a change of phase 

 at the moment of reflexion. The amount of this change is deduced, 

 by a train of the most ingenious reasoning, from the general ex- 

 pressions. Now when a ray, polarized in any azimuth, is incident 

 upon the reflecting surface at an angle greater than the angle of 

 total reflexion, it may be resolved into two one polarized in the 

 plane of incidence, and the other in the perpendicular plane. The 

 intensities of these two portions will not be altered by reflexion ; 

 but their phases will, and each by a different amount. The re- 

 flected vibration, therefore, will be the resultant of two rectangular 

 vibrations differing in phase. This vibration, consequently, will 

 be elliptic, and the reflected light will be ellipticaUy-polarizcd. 

 When the azimuth of the plane of polarization of the incident ray 

 is 45, the intensities of the resolved portions are equal ; and if, 

 moreover, their difference of phase, after reflexion, is equal to a 

 quarter of an undulation, the ellipse will become a circle, and the 

 light will be circularly-polarized. 



Eeducing his formulae to numbers, in the case of St. Gobain glass, 

 Fresnel found that the difference of phase of the two portions of the 

 reflected light amounted exactly to one-eighth of an undulation, 

 when the angle of incidence was 54 37'. Polishing, therefore, a 

 parallelepiped of this glass, whose faces of incidence and emergence 

 were inclined to the other sides at these angles, it followed that a 

 ray incident perpendicularly on one of these faces, and once re- 

 flected at each of the sides, should emerge perpendicularly at the 

 opposite face, 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 polarized in a plane inclined at an angle 

 of 45 to the plane of reflexion, the emergent light will be cin-n- 

 lat-ly-polarized. This was found to be the case on trial ; and the 

 parallelepiped thus constructed and which is known under the 

 name of Frcsnel's rhomb is of essential service in experiments on 

 -circular and elliptic polarization. The results of this remarkable 

 theory have been confirmed by Fresnel by other well-chosen ex- 

 periments ; so that, although the reasoning on which it is based is 

 far from rigorous, there can remain little doubt of its general truth. 

 Fresnel was himself fully aware of the incompleteness of his solu- 



