1 72 TRANSVERSAL VIBRATIONS I 



demonstration which holds good, whatever be the magnitude 

 and direction of the propagated vibration, or, in other words, 

 whatever be the intensity and plane of polarization of the 

 light. The problem which we have now to consider is that 

 which proposes to determine the latter quantities, or to 

 deduce the intensities and planes of polarization of the re- 

 flected and refracted pencils, those of the incident pencil being 

 given. 



This important problem was solved by Fresnel, upon the 

 following principles : 



I. The movements of the molecules of the ether, in a di- 

 rection parallel to the separating surface of the two media, 

 are unaltered ; and, consequently, the resolved parts of 

 the vibrations parallel to that surface are equal in the two 

 media. 



II. The known law of the vis viva holds in the reflexion 

 and refraction of light ; from which it follows, that the masses 

 of ether put in motion, multiplied by the squares of the 

 amplitudes of vibration, are the same before and after re- 

 flexion. 



III. The densities of the ether in the two media are as 

 the squares of their refractive indices. 



(184) Let v and w denote the amplitudes of the reflected 

 and refracted vibrations, that of the incident vibration being 

 taken as unity. When the light is polarized in the plane of 

 incidence, these three vibrations are all parallel to the bound- 

 ing surface, and to one another. Hence, the first principle 

 gives, in this case, the simple condition 



1 + v = w. 



On the other hand, the law of the vis vim furnishes the 

 relation 



m 



