REFLEXION AND REFEACTION OF POLARIZED LIGHT. 93 



however, the author had considered only the case of perpendicular 

 incidence, or the law of propagation of a plane wave parallel to 

 the bounding surface of the two media. In a subsequent memoir, 

 to which I have already alluded, and which was read to the 

 Academy in the year 1823,* he has resumed the problem gener- 

 ally, and examined the modifications produced in the intensity as 

 well as the direction of a wave, or series of waves, in passing from 

 one fluid to another of the same elasticity, but of a different den- 

 sity. The expressions obtained for the intensity of the reflected 

 and refracted waves are functions of the angle of incidence, and of 

 the ratio of the velocities of propagation in the two media. When 

 the wave is incident upon the surface of the denser medium, the 

 expression for the intensity of the reflected wave vanishes at a cer- 

 tain angle, whose tangent is equal to the ratio of the velocities of 

 propagation. At this angle, which is the angle of complete polari- 

 zation, objects should therefore cease to be visible by reflected 

 light ; a ^result which is contradicted by all experience, and is 

 only true when the light is polarized in a plane perpendicular to 

 the plane of reflexion. When the wave is reflected at the surface 

 of the rarer medium, there are two expressions for the intensity, 

 for incidences above and below the limiting angle of total reflexion, 

 respectively. There are also in this case two angles of evanescence. 

 These conclusions, which apply to the case of sound as well as 

 light, are sufficient to show the physical inapplicability of the 

 theory. 



The theory of waves, however, when combined with the prin- 

 ciple of transversal vibrations, has afforded the complete solution 

 of the problem we have been considering. In this development 

 of his theory the character of Fresnel's genius is strongly marked. 

 Our imperfect knowledge of the precise physical conditions of the 

 question is supplied by bold, but highly probable assumptions : the 

 meaning of analysis is, as it were, intuitively discerned, where its 

 language has failed to guide ; and the conclusions thus sagaciously 

 reached are finally confirmed by experiments chosen in such a man- 

 ner as to force Nature to bear testimony to the truth or falsehood 

 of the theory.f 



* Only a portion of this memoir has been printed in the Memoirs of the Institute, 

 under the title " Memoire sur le Mouvement de deux Fluides elastiques superposes," 

 torn. x. 



t Fresnel's theory of reflexion is contained in a memoir read to the Academy of 



