( 383 ) 



allowed to place them here side by side, after which I siiall give 

 some expressions which enable us to determine the optical constants of 

 a metal from the quantities measured, and also some approximative 

 formulae for the calculation of the principal angle of incidence ƒ 

 and principal azimuth H from n^ and k^. 



Light polarized // plane of incidence. 

 Reflection by 

 transparent bodies metals 



Intensity 

 Incident light Reflected light 



sbi\i-r) ^ _ {cosi—]/'n'—sm'iy-\-k' 



sln''{i-\-r) ^ ~~ {cos i+ \/ n"" — sin'' ly +^ 



Difference of phase with incident beam 



-inno 2kcOSi 



180° tgtp^, = — 



l — n'—k' 



Light polarized i plane of incidence 

 Intensity 



tif{i—r) n^cos\i—a)-\- k'cosH i 



tg''{i—r) n'cos\i^a)^^k\os-i ^ 



Difference of phase with incident beam 



0° for 0°<i<7 _ 



180° „ /<f<90° ^^'^ ""^ 



2A;(/t--fw"c'0s-« — sbi^i) cos i 



(F - n^cos^u - sin^i)cos-i - ii^cos^a cos 2i-P 

 From this follows also: 



2k sin i tg i 

 n cos a — tg^ I sin^ i -j- Ir 

 11 and h apply to the disturbance in the metal, arising from plane 

 waves, which fall on the metal with an angle of incidence /. The 

 angle of refraction « is determined by Sin a = Sin i : n. 



7. The expressions obtained are in perfect harmony with those of 

 Cauchy. First the relations of § 6 may be brought to the same form 

 as these. For this purpose we put in accordance with Bekr ^) : 



n cos a :=^ [/ n^ — Sin'' i =z U cos u , k =: U Sin u . . (13) 



Substituting this we get 



cos^ i -j- U'^ — 2 U cos i cos u 



Ml, ^z: ; ; . 



cos'' i -\- U^ -\- 2U cos i cos u 

 Put 



1) Beer, Pogg. Ann. 93, 413, 1854. 



