Second Surface of a Thin Plane Parallel Plate. 31 

 , , « 2 Y2 —fW* n " _ ^372 - «273 



Ps == Pp — 



«272 t- ^373 a 372 + *273 



and j iL _4*i7Jnq-cK) 



ke lL = e a 



n is the index of refraction of the glass, n(l— iK) the index 

 of refraction and absorption for the film, I the thickness of 

 the film, and X the wave-length of the light in question 

 in air. 



When the silver film was thick, the relative phase- difference 

 showed no effect due to the silver-air surface, but was the 

 ordinary phase-difference produced by reflexion in glass on a 

 silver mirror. When the film was thinner, however, there 

 was a marked deviation from this curve. Instead of studying 

 the relative phase-difference produced by the film, we studied 

 the deviation of the relative phase-difference from the ordinary 

 o-lass-silver curve, or in other words the effect of the " thin- 

 ness." The formula for the deviation is the difference of the 

 tan- 1 sin (7) and (8), P-S. 



It has been found by different observers that the optical 

 constants of silver in thin films are different from the values 

 obtained by Drude from observations on silver in mass. This 

 may be due to the thickness of the film being comparable 

 with the mean free path of the free electron. Fortunately 

 this difference affects only one of the functions p s ", p s &c. 

 appreciably, namely A/ 7 . It was found P could be dis- 

 regarded in comparison with S ; also that 2A/ was equal to 

 A s to a sufficiently high degree of aproximation. This 

 simplifies the formula for the deviation to 



1 fr/,V sin(A,"-L) 

 tan rs-tkdM" cos (A s " -L) ' 



The variation of k and L with the angle of incidence could 

 be disregarded. As a result of trials, the values nK = 3*67 

 and ?2 = 0'61, as against Drude's ^K = 3'67 and 72 = 0*18, were 

 found to give the best results. Six series of observations on 

 the deviation are given in the next table, together with the 



theoretical value calculated for the values — = 0'070 and 



0'055 and the values of d s 2 and r s " used in the calculation. 



When we compare the experimental and theoretical results, 

 there is not much similarity. The deviation is in the right 

 direction and has its maximum near the proper place, but 

 the shapes of the curves are different. We cannot improve 

 matters by taking into account the terms that we have dis- 

 regarded. The agreement — such as it is — is the best that 



