524 The Electromagnetic Theory of Light [OH. xvm 



We have ^"l+a + ^g' 



so that P 2 = n v /Q2 = ^~~n v j52 (577), 



shewing that p < 1, as it ought to be. Also 



% = tan" 1 tan" 1 = tan" 1 ^ -^ . 



603. Experimental determinations of the values of p and % have been 

 obtained, but only for light incident normally. For this reason we shall 

 only work out the analysis for the case of = 0. and we accordingly replace 

 equation (576) by the simpler equation 



It is now a matter of indifference whether the light is polarised in or 

 at right angles to the plane of incidence ; indeed, it is easily verified that 

 the same values for p and ^ are obtained in either case. 



Taking, for simplicity, the analysis appropriate to light polarised in the 

 plane of incidence, we have 



, K, X'MF , . 



it? j^ = -jr~ + ~ W ........................ (578) 



K^ K! tprJTi 



from equation (574). 



Since u - a + ift t this gives at once 



2 -/3* = ' .............................. (579), 



604. Let us consider first the results as applied to light of great wave- 

 length. In the limit when p is very small, a/3 is seen to be large in 

 comparison with a 2 -/3 2 . Thus a becomes nearly equal to @, and the 

 numerical value of either is given by the approximate equations 



<> 



When a and ft are equal and large, equation (577) becomes 



- ...(582). 



a 



Now if R denote the reflecting power of a metal, then the intensity of 

 reflected light corresponding to an intensity of 100 in the incident beam, is 

 100 -B. Thus 



100 - R = 100 p 2 



100-200 J ..................... (583), 



