408 Dr. Oliver Lodge on Opacity. 



gives (1/200) 2 ; so even now a metal calculates out too opaque, 

 though it is rather less hopelessly discrepant than it used to 

 be. The result, we see, for the infinitely thin film, is inde- 

 pendent of the frequency. 



Specific inductive capacity has not been taken into account 

 in the metal, but if it is it does not improve matters. It 

 does not make much difference, unless very large, but what 

 difference it does make is in the direction of increasing 

 opacity. In a letter to me Mr. Heaviside gives for the 

 opacity of a film of highly conducting dielectric 



^=£ L (l + 27r f JLkvz)* + (imcz I j/v) 2 } , . . (16) 



where I have replaced his %fivzK.p last term by an expression 

 with the merely relative numbers K/K and /j,//j, , called c 

 and m respectively, thus making it easier to realise the 

 magnitude of the term, or to calculate it numerically. 



Theory of a Slab. 

 An ordinary piece of gold-leaf, however, cannot properly 

 be treated as an infinitely thin film ; it must be treated as a 

 slab, and reflexions at its boundaries must be attended to. 

 Take a slab between x = and x=l. The equations to be 

 satisfied inside it are the simplified forms of the general 

 fundamental ones 



-£-»*; . -§ ME < 



k being l/<r, and K being ignored ; while outside, at # = Z, 

 the condition E=yLtvH has to be satisfied, in order that a 

 wave may emerge. 



The following solutions do all this if q 2 = ^irfxkp : — 



V qv —p J 



p \ qv—p J 



Conditions for the continuity of both E and H at x = 

 suffice to determine A, namely if E x Hj is the incident and 

 E 3 H 3 the reflected wave on the entering side, while E H 

 are the values just inside, obtained by putting <r = in the 

 above, 



Ei + E 3 = E , 



E 1 -E 3 =^(H 1 + H 3 )=^H . 

 Adding, we get a value for A in terms of the incident light E l5 



2E 1 p(qv-p) = A{(qv+pye 2ql -(qv-p) 2 }. 



