JAMIN ON METALLIC REFLEXION. 99 



„ t 



X = COS « COS 2 TT =i, 



y = sin « cos 



(2^4+0- 



These two beams fall on the second surface whose plane of 

 incidence makes an angle («j) with the first ; they give rise to 

 others, polarized in the principal planes of the new plate, and 

 whose vibrations are represented by 



y = A'cos (2t^ + 8'Y 

 y = B'cos(2,r^ + 8"), 



and the diflference of phase of these rays will be expressed before 

 the reflexion at the second plate by the formula 



, .J, -„, sin 8 sin 2 « . > 



tan (8' — 8") = -r— r-— -j. . (14.) 



sm 2 w cos 2 a — sm 2 a. cos 2 w cos b 



We have thus decomposed the ray which has been reflected, 

 a first time, into two beams polarized in the principal planes of 

 the second reflecting surface ; they have, before the reflexion, a 

 difference of route (8' — 8"), and, by the act of the second reflexion, 

 they acquire a new difference of phase (8'"), which is added to the 

 former and gives a total 8' — 8" + 8'". In order that the ray may 

 then be rectilinearly polarized, it is necessary and it is sufficient 

 that 8'-8" + 8"' = ,r, ^^^ich gives 8"' = 7r-(8'-8"). We may cal- 

 culate by formulae (9.), what is the angle of incidence on the 

 second surface which is capable of producing this difference of 

 phase, and it will remain to compare experiment with the cal- 

 culation. 



This comparison has been made for two tables extracted from 

 the memoir of Sir David Brewster, pages 304 et seq. (Philoso- 

 phical Transactions, 1 830.) In the first, relative to silver, the 

 incidence on the first surface is 80°. The angles of the 

 two planes of incidence are written in the first column, and in 

 the following are placed the complements of the incidences which 

 restore the plane polarization. The differences between calcula- 

 tion and observation will be found to be very shght, if we pay 

 attention to the difficulty which must be met with in measuring 

 exactly the azimuths and incidences in such complicated expe- 

 riments. 



H 2 



