106 M. W. Wernicke on the Refractive Indices 



great number of that group of bodies which stand next to the 

 metals in degree of opacity, as the protoxides, oxides, peroxides 

 and chlorides, bromides, iodides, and sulphides of the heavy me- 

 tals. The method depends on the fact that these substances admit 

 of being prepared as uniformly thin layers, which show interfe- 

 rence- colours varying with the thickness of the layer. When these 

 colours are examined by the spectroscope, we see spectra of alter- 

 nate bright and dark bands, from the number and position of 

 which the wave-length of light in the substance, and therefore the 

 refractive index, not only en bloc, but also for the different colours 

 or Fraunhofer's lines, may be deduced. From the comparative 

 perfection of the methods of preparing the thin layers, the accu- 

 racy of the results which this method furnishes depends almost 

 entirely on the delicacy of the balance, which is preferable to any 

 indirect method of determining the thickness of the layers. 



I. 



To determine the wave-length from the position of the maxima 

 or minima in the spectrum, it is first of all necessary to deduce 

 the equations subsisting between these magnitudes with regard 

 to elliptical polarization and absorption. As the interference- 

 bands in the spectrum are best observed in reflected light with 

 perpendicular incidence, I give the complete formulae for this 

 case only. 



If e denotes the thickness of a thin layer of the substance to 

 be investigated, attached to a metal, then, according to the theory 

 of the colours of thin plates, the intensity of reflected light with 

 perpendicular incidence is 



_ (r + /p) g -4r/psin 8 D 

 r ~ (H-rp) 2 -4/y>8in 2 D (i 



In this expression r and p denote the amplitudes of the light 

 reflected from the layer into the air and from the metal into the 

 layer, when the amount of incident light is put equal to 1. r is 

 always positive, p only when the refractive index of the layer lies 

 between the indices of the two bounding media, usually air and 

 metal ; p is negative when it is greater or less than each of the 



(^ 5s \ O 



which X is the wave-length of light in the substance, and S„ 

 S q denote the retardations which the light undergoes by reflection 

 at the metal surface — that is, the reflection and refraction at the 

 limit of the substance and the air. 



Formula (1) presupposes that the material of the thin layer is 

 perfectly transparent; in order to apply it to bodies which, 

 although thin, exert an appreciable absorption on light, the 



' ^, in 



