114 DIFFRACTION. 



elusions arrived at in (106). Accordingly, if c denote the 

 breadth of the obstacle, and b its distance from the screen, 

 the distance, #, of any band from the centre of the sha- 

 dow is 



nb\ 



x = 



2c 



(128) The positions of the fringes formed by a narrow 

 rectangular aperture are determined by a similar formula. 



Let PP X be the section of the aperture, PAP X the portion 

 of the wave which has just reached it, diverging from the lu- 

 minous origin at ; and let QQ' be the projection of the 

 aperture on the screen. Then, if we take the point E on this 

 screen in such a man- 

 ner, that the difference 

 of its distances from 

 the edges of the aper- 

 ture, EP'-EP, shall 

 be equal to a whole 

 number of semi-undula- 

 tions, that point will be the centre of a dark or bright band, 

 according as the assumed number is even or odd. For, in the 

 former case, the wave PAP 7 may be divided into an even 

 number of parts, such that the distances of every two conse- 

 cutive points of division from the point E differ by half an 

 undulation. The waves sent by every two consecutive por- 

 tions to the point E will therefore be in complete discordance, 

 and the total effect at that point will be null. On the other 

 hand, when the difference EP X - EP is equal to an odd num- 

 ber of semi-undulations, the number of opposing portions of the 

 wave will be odd, and as the alternate portions compensate 

 each other's effects at the point E, there will remain one por- 

 tion producing there its full effect. 



The successive bands being formed at the points for which 



