DIFFRACTION. 121 



effect of that portion of the incident wave would be null at the 

 point Q, and no light from it would reach the eye. The 

 effect of the grating, however, is to intercept the whole or 

 part of one of the two interfering portions, and thus to render 

 the other visible : and this effect is greatest when the opaque 

 and transparent parts of the grating are equal. A bright 

 band will therefore be visible in the direction Q,". The same 

 thing will happen for all the similar divisions of the grating, 

 the distances of whose extremities from the point Q differ by 

 two, three, or any whole number of undulations ; and thus 

 there will be a succession of bright bands, visible at different 

 angular distances from the direct ray PQ,. 



These angles are easily computed. Let a'k be the arch of 

 a circle described with the centre Q, ; then a"k = a' a" cos a'a"k 

 = a'a'sin PQa". But the interval of retardation, a^k, is equal 

 to the length of a wave ; so that, if the angle PQa" be de- 

 noted by 0, and the interval composed of an opaque and trans- 

 parent part of the grating a' a", by 6, we have 



sin0 = -. 







This is the angular distance of the first bright band from the 

 central one ; and it is obvious that the corresponding angle, 

 for the band of the n th order is given by the formula 



The position of each ray, in these spectra, therefore de- 

 pends solely on the length of the wave and is independent of 

 the nature of the substance by which it is produced. 



(134) It is a remarkable circumstance of the phenomenon 

 whose laws we have been tracing, that when the experiment 

 is performed with the requisite care, the several species of 



