384 ELLIPTIC POLARIZATION. 







When the angle of incidence exceeds the angle of total 

 reflexion (the light passing from the denser into the rarer 

 medium), the expressions for the amplitudes of the reflected vi- 

 brations, given in (184, 5), "become imaginary. But it is obvious 

 that, in this case, the intensity of the reflected light is simply 

 equal to that of the incident, there being no refracted pencil. 

 How, then, are the imaginary expressions to be interpreted ? 

 They signify, according to Fresnel, that the periods of vibra- 

 tion 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 has been deduced 

 by Fresnel, by an ingenious train of reasoning, based upon 

 the interpretation of imaginary formulae. It varies with the 

 incidence ; and is different for light polarized in the plane of 

 incidence, and in the perpendicular plane. 



In the case of light polarized in any azimuth, we have only 

 to conceive the incident vibration resolved into two, one in 

 the plane of incidence, and the other in the perpendicular 

 plane. The phases of these vibrations being differently 

 altered by reflexion, the reflected vibration will be the re- 

 sultant of two vibrations at right angles to one another, and 

 differing in phase, the amount of the difference depending 

 upon the angle of incidence : this vibration, consequently, 

 will be elliptic, and the reflected light elliptically-polarized. 

 When the azimuth of the plane of polarization of the incident 

 ray is 45, the amplitudes of the resolved vibrations will be 

 equal ; and if, moreover, their difference of phase is a quarter 

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

 light will be circularly-polarized. 



(196) Eeducing his formulae to numbers, in the case of 

 St. Grobain's glass, Fresnel found that the difference of phase 



