VI. LAWS OF REFLEXION FROM METALS. 



[Proceedings of the Royal Irish Academy, VOL. i., p. 2. Read Oct. 24, 1836.] 



THE author observes that the theory of the action of metals 

 upon light is among the desiderata of physical optics, whatever 

 information we possess upon this subject being derived from 

 the experiments of Sir David Brewster. But, in the absence of 

 a real theory, it is important that we should be able to represent 

 the phenomena by means of empirical formulae ; and, accord- 

 ingly, the author has endeavoured to obtain such formulae by 

 a method analogous to that which Fresnel employed in the case 

 of total reflexion at the surface of a rarer medium, and which, 

 as is well known, depends on a peculiar interpretation of the 

 sign \/ - 1. For the case of metallic reflexion, the author 

 assumes that the velocity of propagation in the metal, or the re- 

 ciprocal of the refractive index, is of the form 



m (cos x + \/ - 1 sin \) ; 



without attaching to this form any physical signification, but 

 using it rather as a means of introducing two constants (for 

 there must be two constants, m and x> for each metal) into 

 Fresnel's formulae for ordinary reflexion, which contain only 

 one constant, namely, the refractive index. 



Then if i be the angle of incidence on the metal, and i' the 

 angle of refraction, we have 



sin i' = m (cos \ + y - 1 sin x) sin ?', (1) 



