JAMIN ON METALLIC REFLEXION. 6/ 



4. When polarized light is reflected several times from parallel 

 metallic mirrors, at the incidence of maximum polarization, the 

 polarization is restored after an even number of reflexions. 



5. Finally, the reflected beam becomes again polarized after 

 an even or uneven number of reflexions under a great number 

 of incidences, determined by laws which remain to be found. 



Since a ray polarized in any plane before incidence may always 

 be decomposed into two others polarized in azimuths of 0° or 

 90°, which, according to Sir David Brewster, do not change their 

 azimuth by reflexion, the reflected ray will always be formed by the 

 superposition of two rays polai-ized in these principal azimuths ; 

 and its state of vibration will be known, if we have found out 

 beforehand the modifications undergone by the component rays 

 during reflexion. The first question therefore to be answered is 

 this : What transformations occur, during reflexion, in rays po- 

 larized in the principal azimuths ? 



Now every polarized ray which undergoes any action without 

 losing its polarization and without changing its azimuth, can 

 only be affected by changes of phase and variations of intensity : 

 we have therefore to examine if these modifications occur, and 

 according to what laws they are produced, for two rays polarized,' 

 one in the azimuth of 0'^ and the other in the azimuth of 90°. 

 This is the investigation we are about to commence, beginning 

 with the determination of the intensities. 



IV Measure of the Intensity of Light reflected by Metals. 



If we cause rays polarized in the azimuths of 0° or of 90° to 

 fall on a plate of glass, the intensities of the reflected beams will 

 be represented by the following formulae of Fresnel : — 



T,2_ sin^(l-^) T,2_ tan^(l-^) /, x 



~sin2(l+r)' ~tan^(l+r)' * * ' ^ ' 



These formulae, verified by MM. Arago and Brewster, are 

 recognised at the present day by experimenters : they will serve 

 us as a starting-point for measuring the quantities of light P and 

 J^ reflected by metals ; in order to which it will suffice to com- 

 pare P and I'^ on one side, and J^ and J'^ on the other. 



To make this comparison, let us place in contact two plates, 

 the one of glass, the other of metal, so that the two polished faces 

 may be in the same plane and the two plates form one reflecting 

 surface, of which one portion is glass and the other metal : then 



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