Dr. Oliver Lodge on Opacity, 401 



Opacity of Gold-leaf. 



Now returning to the general solution (5) let us apply it 

 to calculate the opacity of gold-leaf to light. 



Take cr = 2000fJL square centim. per sec, 



p = 2irX 5 X 10 14 per sec. ; 



then the critical quantity 47r/pcrK or (7) is 

 2x9 xlO 20 1800 



5xl0 14 x2000K/K K/K * 



This number is probably considerably bigger than unity 

 (unless, indeed, the specific inductive capacity K/K of gold 

 is immensely large, which may indeed be the case — refractive 

 index 40, for instance, — only it becomes rather difficult to 

 define) ; so that, approximately, 



// 27rup \ /40 x 5 x 10 u ,. n „ . n R 



« = V (-jF) = V 2000 = ^ 10 = 3 x 106 ; 



or the damping distance is 



F x x 10~ 5 centim. = j microcentimetre, 

 whereas the wave-length in air is 



6 x 10~ 5 centim. = 60 microcentimetres. 



The damping distance is therefore getting nearer to the 

 right order of magnitude, but the opacity is still excessive. 



A common thickness for gold-leaf is stated to be half a 

 wave-length of light ; that is to say, 90 times the damping 

 distance. Hence the amplitude of the light which gets 

 through a half- wave thickness of gold is e~ 9o of that which 

 enters ; and that is sheer opacity. 



[Maxwell's calculation in Art. 798, carried out numerically, 

 makes the damping 



_ 2tt\xg 



e * x , = exp. (— >10 8 #) for gold, 



see equation (8) above ; or, for a thickness of half a wave- 

 length, 10 -1000 , which is billions of billions of billions (indeed 

 a number with 960 digits) times greater opacity than what 

 we have here calculated, and is certainly wrong.] 



It must, however, be granted, I think, that the green light 

 that emerges from gold-leaf is not properly transmitted ; it 

 is light re-emitted by the gold *. The incident light, say the 



* This would be fluorescence, of course ; and Dr. Larmor argues in 

 favour of a simple ordinary exponential coefficient of absorption even in 

 metals. See Phil. Trans. 1894, p. 738, § 27. 



