DIFFRACTION. 115 



RP X - RP = n\, it is obvious that their, distances, RB, from 

 the centre of the projection of the aperture, will be given by 

 the same formula as in the case last considered, c being now 

 the breadth of the aperture, with this difference, however, 

 that the dark bands correspond to the even values of n, and 

 the bright bands to the odd values, which is the reverse of 

 what takes place in the bands formed within the shadow of an 

 opaque obstacle. We learn then, 1st, that the distances of 

 the successive fringes of any colour form an arithmetical pro- 

 gression whose common difference is equal to its first term ; 

 2ndly, that they vary directly as the distance of the screen, 

 and inversely as the breadth of the aperture ; and 3rdly, that 

 they are proportional to the length of the wave ; and there- 

 fore greatest for the extreme red rays, least for the extreme 

 violet, and of intermediate magnitude for the rays of inter- 

 mediate refrangibility. 



"We have supposed the screen to be so remote that the 

 bands are entirely icitliout the projection of the aperture. 

 This will obviously be the case when UP' - QP is less than 

 half a wave. When the distance of the screen is so small that 

 QP X - QP exceeds this limit, fringes will be visible also within 

 the projection of the aperture. In this case the portions into 

 which the wave is divided are sensibly different in magni- 

 tude as well as obliquity. The reasoning above employed 

 is therefore no longer applicable ; and the points of maximum 

 and minimum brightness can only be obtained by a complete 

 calculation of the intensity of the light. 



(129) The phenomena of diffraction hitherto considered 

 are of the simplest class ; but as such phenomena arise in 

 every instance in which light is in part intercepted, it is ob- 

 vious that they admit of endless modifications, varying with 

 the form of the interposed body. Some of these are too re- 

 markable to pass unnoticed. 



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