338 Mr Glazebroo'k, On the Reflexion [Feb. 9, 



The surface conditions give 



K sin Xo + /^i sin (%„ + O = «' ^in (%o + (^3), 



-p{/ccosxo-/^icos(p^, +ej] 



= - ;g /^ p sm (xo + e ) ; 

 hence, since 



p = p' and -^ = /x^ 



cos {/c cos p^„ - K^ cos (xo + ej} 



= -«>V[/^'sin'^-l}sin(xo4-e') ,...(24). 



Thus 



K+ K^ COS e^ = «' cos e . 



K^ sin gj = K sin e', 



cos (f) {k — K^ COS ej 



= — Kfx /^{/J' sin^ ^ - 1) sin e', 



/c^cos <^ sin Sj = — k'/j, /^{jj? sin^ </> — !) cos e'. 

 Solving 



cos' (^ + /Lt' - /A* sin' (^ . _ „. 



/c, cose =a: — ^-r — ^^- — 4 . .> , (2d), 



^ ^ cos (j) — /J, + fur snr (f) ^ ' 



^ sine --^^^-^'^''t^-^-°'^ (261 



''^'''''^" cos>-yc.' + /x^sin'(^ ^^^^' 



tane,= - '^T/^y"^^^~'^ (27), 



^ COs'^ + yLi'-yU, Sin'0 ^ ^' 



whence 



tanU= ^V(/i'sin'(6-l) (28). 



" ^ cos 9 



This agrees with Fresnel's formulge for light polarized per- 

 pendicular to the plane of reflexion. 



And as before k^= k, or all the energy in the incident wave 

 has been transferred to the reflected. 



Thus if we have a wave of polarized light incident so as to be 

 totally reflected and resolve it into two waves polarized in and per- 

 pendicular to the plane of incidence, the difference of phase in 

 the two reflected waves is exactly that given by Fresnel, and the 

 theory on which he based his rhomb still holds. 



