214 Prof. Nihal Karan Sethi on Talbot's Sands and 



the gradation of colour as the dispersion is diminished until 

 the above-mentioned abrupt changes are fully established. 

 If the dispersion is reduced still further, the sequence of 

 colour within a band becomes actually reversed. The edge 

 of an orange band towards the green side becomes distinctly 

 redder, and that towards the red side distinctly more yellow. 

 It is needless to point out that, although the bands retain 

 excellent visibility within a wide range of adjustment, the 

 minima are not absolutely black except at a particular stage 

 which naturally varies from point to point in the spectrum. 

 And it was found that this stage was not identical with the 

 stage which showed the best uniformity of colour within a 

 band, but was slightly different — the dispersion required for 

 uniform colour being less than that necessary for giving 

 absolutely black minima. 



4. Talbot's Bands and tlie Maxwell Colour- Triangle. 



A very simple explanation of the above facts is furnished 

 by the usual method of regarding Talbot's bands as being- 

 produced by the dispersion of the laminary diffraction 

 pattern formed by the mica plate and the aperture, the 

 patterns in different wave-lengths suffering relative shifts 

 depending on the dispersion of the prism. 



The curves in fig. 1 show the intensity of light at various 

 points in the diffraction pattern for wave-lengths, for which 

 the mica plate produces a retardation specified on them. 

 They have been plotted from the well-known expression * 



I=^sin^[l + cos(p~2/^)]. . . . (1) 



If the prism shifts each successive curve to the left by pro- 

 portionate amounts, it is easy to see that the minima A 1? A 2 , 

 A 3 , A 4 , etc. may all be made to coincide. This adjustment 

 will give absolutely dark minima. But it will be observed 

 that in this case the maxima at B T , B 2 B 3 , B 4 , etc. will not 

 coincide because the intensity curves are unsymmetrical and 

 the maxima for shorter wave-lengths will lie more towards 

 the left and those for larger wave-lengths more towards the 

 right. But if the dispersion is a little less (about | of 

 the former), it is possible to arrange so that the maxima B x , 

 B 2 , B 3 , B 4 , etc. may coincide. In this case the minima will 

 not coincide, but between one minimum and another the 

 proportions of the various wave-lengths contributing most of 

 the light will remain fairly uniform, and will give rise to a 



* Rayleigh, loc. cit. 



