161 



with the incidence. It may therefore be worth while to re- 

 mark, that the formula given by Fresnel for reflexion at the 

 surface of a transparent body, though not of course appli- 

 cable, except in a very rude way, to the case of metals, would 

 yet lead us to expect, for highly refracting bodies as the 

 metals are supposed to be, precisely such a result as that 

 obtained by Mr. Potter. For when the index of refraction 

 exceeds the number 2 + \/3, or the tangent of 75°, the ex- 

 pression for the intensity of reflected light will be found to 

 have a minimum value at a certain angle of incidence ; while 

 for all less values of the refractive index the intensity will be 

 least at the perpendicular incidence. 



Let i and i' be the angles of incidence and refraction, 

 and put 



sin i cos i 



M = —. r, fX = T, ; 



sin t cos z 



then if i be the intensity of the reflected light, when common 

 light is incident, Fresnel's expression 



^ ~ ■•^ tsin' [i + i') "^ tan''(i + i')) ' 

 in which the intensity of the incident light is taken for unity, 

 may be put under the form 



-,-A + 



which has a minimum value when 



1 18 



M+-= M + r; 



' M 



the value of i being in that case 



,_ ("-D--t _ (" + !;)' - 8 



