600-602] Metallic Media 523 



Thus in x centimetres the decay in the amplitude is represented by a 

 factor e~ ax or e~ rixlofix , shewing that in a good conductor a wave of light 

 would be practically extinguished before traversing more than a small 

 fraction of a wave-length. This prediction of the theory is not borne out 

 by experiment (see below, 605). 



Metallic Reflexion. 



602. Let us suppose, as in fig. 137, that we have a wave of light inci- 

 dent at an angle 6 l upon the boundary between two media, and let us suppose 

 medium 2 to be a conducting medium of inductive capacity K 2 '. Then (cf. 

 599) all the analysis which has been given in 590 593 will still hold if 

 we take K 2 to be a complex quantity given by 



(574). 



Since K 2 is complex, it follows at once that V 2 is complex, being given by 



C' 2 



V 2 - 



2 17" ' 



^-2/^2 



and hence that the angle # 2 is complex, being given (cf. equation (557)) by 



(575). 

 22 



The value of u is now given, from equation (562), by 



2 _ K 2 yuj cos 2 2 



~ JL K COS 2 



( 5 76) 



(cf. equation (575)) for light polarised in the plane of incidence. For light 

 polarised perpendicular to the plane of incidence, the value of u is found, 

 as before, by interchanging electric and magnetic symbols. 



If we put u = a + i@, we have, as before (equation (565)), 



If we put this fraction in the form pe 1 *, then the reflected wave is 

 given by 



_ 7'J*i(-a; cos fli 



so that there is a change of phase K^ at reflection, and the amplitude is 

 changed in the ratio 1 : p. The electric force in the refracted wave is 

 accompanied by a system of currents, and these dissipate energy, so that 

 the amplitude of the reflected wave must be less than that of the incident 

 wave. 



