Fresnel's Reflexion of Light TJieory. 



319 



ordinary transparent media. In this connexion, it is of 

 interest to find that so long a^o as 1830 Mr. Potter discovered 

 that the light reflected by steel diminishes with increase of 

 i for a considerable range from normal incidence. 



The transference of the formula from the incident ray to 

 the ray refracted into a plane-parallel plate is necessarily 

 somewhat tedious in the case of common light. When fi is 

 the index of the second medium with respect to the first, fi~ l 

 is the index of the first with respect to the second. Assum- 

 ing /x>l, the + sign of s/ q has to be adopted in the % value 

 and we have l//*th the incident ray reflected when 



p 2 + 1 + / p+ v/ g) 2 -yV-l) 2 



si* • == v o?Ti± v /p+v / ^) 2 - 4 (^- 1 ) 2 ~' 



Multiplying the numerator and denominator in the surd by 

 (/jl 2 -\-1± ^p — y/qf, we obtain 



' V [(^*H-l± v / 1? )»- 9 J»-4(n-l)>»+l± y/p- Vqf 

 But, g=G*' + l± s/pf-^\n-V)\ 



therefore the term 



[P 2 +i± /p) f -^=iV(»-i) 4 



and 



Sini = A / V(n- l)^-^(^ 4- 1 + y/^-y/y) 2 



Multiplying the numerator and denominator in the surd by 

 — /£~S taking care to include %/ ' p and ^q in the operation, 

 we get 



si 



n ; = A / Q- 2 +l± y/ p-xA)V-4(n-l ) 2 

 V ( /1 -* + l ±v / i ,_^ ) *_4 l „-l/ 



V: 



, 2fM- 2 (n-l) 





>- 2 +i±v^-^ Y i 



and /x -1 sin i = sin r } therefore 



+ l± ^-y/g V 1 

 2^- 2 (;i-l) /_ /x J 



■i±A/p-A/gyi _ 



^" 2 (n-l) ; /* 



ft- 



