AT THE SURFACE OF AN UNCRYSTALLIZED BODY. 25 



Now, by Article (26), we must suppose that «a and v" are very large compared with 



V and «', and consequently that s.^ and «", and therefore ij, are impossible quantities. Let us 

 accordingly put 



= tan\/,\/ - 1 (I), , = tan o) \/ - 1 (2), 



HS - s flS + ■ 



and we then have 



„ IJ.S — s' cos w ,, ^ ^— 



F = ; g-(*+")V^ Y 



' fiS + s' cos \|/ 



Now this value of F^ indicates, as in Section iv, that the intensity of the reflected ray is 

 lus-s' costtiT (iis-s'y-ti- 



[us + S' COS\//j (/!« + s)^ - »)^ 



And that its phase differs from the phase of the incident ray by the quantity (-^ + to). 



/ I pv"\'^ v' J ij" 



To calculate >;, we observe that s" = \/ 1 — I = p — v— 1 very nearly, since — is very 



large: and similarly, «2 = — p — \/— 1. We here give s" and s.^ opposite signs, because the ex- 



v 



pressions for F, and V" will contain the factors e^^'-'^'^ and e''s':'^^*. Now one of these 

 (namely, F") ought to diminish rapidly as z increases, and the other (Fj) ought to do so as x 

 decreases ; but this cannot be if s" and Sj have the same sign, therefore we must take these 

 quantities with different signs. 



p pv" 



Hence ,, = (,;= - 1) (,x= - 1) • 



V 



and therefore, since y = _ ^ we have 



V 



, f/ - 1 ;U= - 1 P 



If we suppose the light to be incident at the polarizing angle, the expression for the intensity 

 of the reflected ray becomes (since at that angle us = s' = p) 



W + 1 2,1 j 



' ip' - t]' I v' - 1 ,i' - iV' 



For common plate-glass we may put f* = - , and therefore I ) = - nearly ; and for 



2 V 2^ / 6 ■ 



12 /^^ - IN'' 



diamond we may put ju = — , and therefore -j =i very nearly. Hence, supposing that 



V is the same for both, the intensity of the reflected ray at the polarizing angle is about six 

 times greater for diamond than for plate-glass. Hut we have every reason to suppose that v 

 (the index of refraction for normal waves) ami /i (that for transversal) will increase together. 



■ See the procesH of superposition in Section IV. 



Vol.. VII. Part I. D 



