1880.] and Refraction of light. 837 



Solving these equations, we get 



/i' cos 20 + 1 

 K^coQe^=ic'^~~^j-^ (20), 



2ya cos (^ v/(/^' sin' (^ - 1) 



K. sme, = — K— — 7. — (21), 



* /"-' ~ 1 



.. = -tan- ^^°°^f^(^'r'f-^' 



' /i^ cos 2(/) + 1 ^ ' 



Green's formulae for light polarized in the plane of incidence is 



^ yU, COS (p 



and this agrees with the result above. 



Also squaring and adding (20) and (21) 



^ = K^, 



or the amplitude of the reflected wave equals that of the incident. 



Now let the vibrations be perpendicular to the plane of in- 

 cidence. 



The equations are 



df ~ KM'^dzV' 



df " \dx' "^ dz'J ' 

 u = u' = 'w = w' = 0, 



V = V, 



j)dv _j,, dv 

 dx dx ' 



and the solution as before can be written 



'Ix 



V = K sin {^-\-hz — t\ 

 + «jSin (-■Tf+ hz -t + eA , 



Vx 



v = k'c ^' sin {hz — t + e) 

 where Z'^ = //,V — 1 



= /jb" sin^ (ji —1. 



25—2 



