( 382 ) 



V = 2jr : 7Y^^i'+(/j*. Let the velocit}^ of light in the air be V, the 

 index of refraction of the perfectly transparent medium n, then : 



From (12) follows, that for a metal q^ =p q)^ occurs instead of q^ 



and the quantity q^ q= qj^ for q^. Let n„i be the quantity, which for 



a metal corresponds to the index of refraction n of the perfectly 

 transparent medium, then 



The cosines of the angles formed by the normals of the planes 

 of equal amplitude and phase with the ^Y and ^-axis, are respectively : 



Pi ' i^Pi'^P," ' P, ' VPx-^P^^ and ^1 : V^lx-^q^^ » ?2 '- i^^T+ï,' 

 With observance of the above given values of F and Q and in- 

 troduction of the angle a between the planes of equal phase and 

 ampHtude Piqx-\-p^q^ = PQ cos a. Thus : 



«;, = -^ {-P^ -VQ'^ 2iPQ cos a), 



or according to (3) and (5): 



4.-1 

 Hence the so-called complex index of refraction of a metal is 



VT 

 n„i= ('='=9') — • Let P-o be the wave length in the metal for light 



entering normally, then according to (1) ^=2jr : XQ=z2jr7io : X and 

 p=2jrko : X, SO nm = ƒ?„ =F '^"o- 



6. It follows from what precedes, that in accordance with Eisenlohr ^) 

 we can deduce the expressions determining the amplitudes for the 

 metallic reflection from those for the reflection on transparent bodies, 

 if we replace 71 by u^ =f d'o- Let the incident beam of light have 

 the intensity 1 and let it be polarized in the plane of incidence. 

 The reflected disturbance may be represented by the real part of 



sin (ï — ?■) _L I TT . • ■ T^ 7 1 *"* ('- ~ *') 



e±^'^^-Ty.'.Heresüir:^sini:n. Tut n =: ;<„ =f «A-„, tiien -^ — -. 



sin {i -\- r) sin {i -{- r) 



passes into Ae±'^. The disturbance reflected by metals is the real 

 part of Ae±''^'^*+'^-~^\ in which A is the ampHtude and B the dif- 

 ference of phase with the incident ray. In this way we arrive at 

 the well known expressions for the metallic reflection. I may be 



1) Cf. also LoRENTz, Theorie der Terugkaalsing en Breking, p. 163, 

 Schlömilch's Zeitsclir., 23, 206, 1878. 



