ON COLOURS IN METAL GLASSES, ETC. 271 



In equation (26), on p. 409,* we have already proved that 



T = I 1 2 - 16^(1 + *") -^./A (9 - \ 



s 



If we write 



M 16n 2 (l + K 2 ) , 



-{(l + n) 2 +nV} 2 

 equation (21) may be written 



T = Mo e -""'"" /A ......... (23). 



Equations (20) and (21) are thus correct within 2 per cent, for directly incident visible 

 light, and for /A = 1 in the case of gold if c/>91ju//, or in the case of silver if 

 (/> 60/J./A, where Ip-p EE 10~" millim. 



For convenience of reference the corresponding results for obliquely incident light 

 are given below. Let be the angle of incidence. When the incident light is 

 polarised in the plane of incidence, the ratios R, T of the intensities of the reflected 

 and of the transmitted beams to that of the incident light are given by 



' 8ay ..... (2o) ' 



where u and v are defined by the equation 



(u, v) cos (9 = [{(nV-1 + sin 2 0} 2 + 4nV} + (n 3 /?^! + sin 2 ^)] 5 . . (20). 

 v 2 



When, however the incident light is polarised perpendicular to tlie plane of 

 incidence, the corresponding ratios are given by 



where 



u'-<.v'={n(l-i K )YI(u-<.v) ........ (29). 



Putting 9 = 0, we obtain 



R = If = H, h T = T' = T , 



u = u' = n, v = v' = HK. 



It appears from equation (23) that the colour of the light transmitted by a metallic 

 film, although principally dependent on the values of nK/k for different values of X, is 

 also affected by the corresponding values of M . The thicker the film, however, the 

 less important is M in determining the colour. 



* 'Phil. Trans.,' A, 1904. 



