INTERFERENCE OF LIGHT. 



85 



first dark band is produced on either side of the central bright 

 one, and at points for which the distances traversed differ by 

 the length of half a wave ; the second pair of dark bands 

 where these distances differ by one wave and half; and 

 BO on. 



(104) In Young's experiment, if the light diverging from 

 the two apertures and O x , 

 be received on a screen, AD, 

 it is found that the central 

 bright band is formed at the 

 point A, where the screen 

 is intersected by the line 

 PA, which bisects the line 00' and is perpendicular to it. 

 The central band, therefore, is formed where the paths traversed 

 by the two pencils are equal. There will be a dark band on 

 either side of the central bright one, and, beyond these, a pair 

 of bright bands. The difference of the distances of one of these 

 from the two apertures, BO' - BO, is a constant quantity, what- 

 ever be the position of the screen ; this difference is the length 

 of a wave. Beyond these is a second pair of bright bands, the 

 difference of whose distances from the two centres, CO X - CO, is 

 double of the preceding, or equal to two whole waves ; and in 

 like manner, the difference of the lengths of the paths, at the 

 place of each succeeding bright band, is an exact multiple of 

 the first difference, or of the length of a wave. 



Similarly, for the intermediate dark bands, the difference 

 in the lengths of the paths, where the first pair is formed, is 

 half the difference, BO X - BO, or half the length of a wave. The 

 differences of the paths, at the place of each succeeding pair 

 of dark bands, are in like manner intermediate to the cor- 

 responding differences for the bright bands on either side, and 

 are odd multiples of half a wave. 



The difference of the distances from the two apertures 



