220 Prof. Nihal Karan Sethi on Talbot's Bands and 



however, the difference in the appearance of the spectrum in 

 the two positions of the plate becomes at once, evident. In 

 the position T 1 of the plate the bands remain as clear as 

 ever, their brightness increasing with the width of the slit, 

 assuming, of course, that the condition for maximum visi- 

 bility has been satisfied, and the colours of the bands change 

 in the manner already considered in the preceding sections. 

 With the plate in the position P 2 , on the other hand, the 

 visibility of the bands in the spectrum at first rapidly 

 diminishes to zero ; the bands then reappear, but with the 

 maxima and minima of illumination interchanged in posi- 

 tion and with greatly diminished visibility. With further 

 widening of the slit their distinctness again falls to zero, 

 reappears again very faintly, falls again to zero, and finally 

 vanishes. 



The reason why, with the plate in one position, the 

 visibility of the bands is unaffected by opening the slit wide, 

 while with the plate in the other position it is so rapidly 

 destroyed, can be readily understood if the ordinary slit of 

 the spectroscope is replaced by one which can be given a 

 slow lateral motion while the rest of the spectroscope remains 

 fixed. It will be observed then, that with the slit narrow 

 and the plate in the position P, the interference bands seen 

 remain stationary as the slit is gradually moved, evidently 

 because their drift in the diffraction-pattern due to change in 

 wave-length is completely compensated by the dispersion of 

 the prism. On the other hand, with the plate in position P 2 , 

 the bands are seen to shift laterally in the field of view, 

 because now the shift and the dispersion are in the same 

 direction, and the latter only helps to increase the former. 

 When the slit is opened wide, the successive appearances 

 seen with a narrow slit in different positions are presented to 

 the eye simultaneously, so that in one position of the plate 

 the bands remain visible, and in the other position they 

 vanish as the result of superposition after one or two faint 

 reappearances and disappearances. 



6. Mathematical Theory. 



The theory of the phenomena described in the preceding 

 section may be worked out on exactly the same lines as in 

 the case of Talbot's bands, except that in the present case 

 the diffraction-pattern admitted into the spectroscope is 

 limited by the width of the slit, and the integration of 

 expression (1) for the intensity in the diffraction-pattern has 



