518 Mr. A. E. Oxley on an Apparatus for the 



then supposing a phase-change to be produced on reflexion, 

 the reflected amplitude may be represented by the complex 

 quantity a+/3t, and the reflected vibration may be written 



where a and ft are real. 

 This may be written 



#v = (« + /&) .e mt 

 al. 



„, „ ,9i int (nt+B).i 



where r= V « 2 + fi 2 } and = arc . tan — • 



Hence we see that a phase-change is produced on reflexion 

 amounting to 6. 



Let ^r be the angle of incidence of a beam of plane- 

 polarized light incident on the surface AB of the rhomb 

 ABCD (fig. 1). 



Fiar. 1. 



# 



If yjr' and fju are respectively the corresponding angle of 

 refraction and index of refraction, then we have 



For total reflexion 

 Writing 



sin yjr = /jL . sin ty' ' . 

 to take place, yjr' will be complex. 



then 



sin ^=fjb . sin ((• + t)l) 



=fi . sin f . cosh 77 + ^ . 1 . cos f . sinh 77. 

 Equating real and imaginary parts, 



{a . l . cos f . sinh 77 = 0, 

 .'. cosf^O or sinh 77 = 0, 



7T 



whence 



7i = gives the ordinary case of refraction. 



Z^2 or 7?==0, 



