460 M. E. Jochmann on the Reflection and Refraction 



cally fluctuating intensity very quickly converges towards the 



mean value 





We have now to determine whether (speaking after the ana- 

 logy of the phenomena of Newton's coloured rings), with a me- 

 tallic layer increasing in thickness from the centre to the circum- 

 ference, the middle appears bright or dark. For A = 0, 



da' 2 

 dA 



*KH QiQt(Qi ~ Qs) sin 2 (e + u) 



L 



fai + tfa)' 



This expression is positive or negative, according to whether 

 the third medium is optically denser or rarer than the first. 

 Thus, for example, with a metallic coating of this kind, of vari- 

 able thickness, adhering to glass, the middle in reflected light 

 must appear dark or bright, according to whether the reflection 

 takes place in air or in glass. If the third medium is identical 



with the first, and so qi = q 3 , then, for A = (), a /2 = and ^-- = 0, 



and the middle appears dark. 



The discussion of the expressions for a' 2 and a y/i 9 leads to per- 

 fectly analogous results. 



As regards the comparison of the given results with experi- 

 ment, hitherto only some of the noble metals, particularly silver, 

 gold, and platinum, have proved capable of being obtained in 

 sufficiently thin, transparent layers. These metals are charac- 

 terized generally by large values of the constant e. For silver, 

 when the reflection takes place in air, Jamin's observations 

 give :— 





tog»x= 



e = 



Ojcos e. 



9 X sin e. 



For Fraunhofer's line D 



» » H 



0-4595 

 0-2740 



79° 15' 

 77 16 



0-5373 

 04142 



2-830 

 1-833 



Quincke's series of observations [Opt. Unters. §§ 39-41) give 

 the following values for the optical constants of thin lainellse of 

 silver and gold with reflection in air and in glass (these observa- 

 tions refer to red light) : — 





Reflection in air. 



Reflection in glass. 



01 



\i. 



tog«r 



€. 



Iog0 3 . 



€. 



Silver on crown glass. 



,, flint glass... 



Gold on crown glass. 



0-5742 

 0-5349 

 0-4016 



87°54 / 

 86 24 

 84 57 



03545 

 0-3764 

 0-2985 



84° W 



81 37^ 



82 43 



1-658 

 1-440 

 1-268 



1-5149 

 1-6258 

 1-5149 



