412 Dr. Oliver Lodge on Opacity. 



The characteristic number which governs the phenomenon 



is — or — -, a number which for light and gold we reckoned as 



being about gL tnat is decidedly smaller than unity, a being 



s /(2wfMkp) or a / ( - 77 ^- ). The characteristic number p/uv 



we will for brevity write as h, and we will express amplitudes 

 for perpendicular incidence only, as follows : — 



Incident amplitude 1, 



externally reflected b= — < -z — \-. r^ \ 



i 1 + (I -h/i) J 



2h 



entering 

 Incident again 1, 



internally reflected e— < — * i ' 



2\/2 

 emergent /= {1 + (1 + fe)2 ^ 



(It must be remembered that e and / refer to the second 

 boundary alone, in accordance with the above diagram.) 



Thus the amplitude transmitted by the whole slab, or 

 rather by both surfaces together, ignoring the opacity of its 

 material for a moment, is 



transmitted cf= ., — / ., ,* 7 NO « 

 1 + ( 1 + A) 2 



To replace in this the effect of the opaque material, of 

 thickness I, we have only to multiply by the appropriate ex- 

 ponential damper, so that the amplitude ultimately trans- 

 mitted by the slab is 



4;\/2.p/uv _ al 

 l+(l+p/*v)* e a 



times the amplitude originally incident on its front face. 



This agrees with the expression (18) specifically obtained 

 above for this case, but, once more I repeat, multiple reflexions 

 have for simplicity been here ignored, and the medium has 

 been taken as highly conducting or very opaque. 



But even so the result is interesting, especially the result 

 for /. To emphasize matters, we may take the extreme case 

 when the medium is so opaque that h is nearly zero ; then b 

 is nearly — 1, c is nearly 0, being hs/2, e is the same as h 

 except for sign, and /is nearly 2. 



