DIFFRACTION. Ill 



And the intensity of the light when the obstacle is altogether 

 withdrawn is 



1 + m - m' + m" - m'" + &o. = 2. 



Now, as the terms of this series are continually decreas- 

 ing, and are affected alternately with opposite signs, it is 

 manifest that if we stop at any term, the sign of the remain- 

 der will be the same as that of its first term, and therefore 

 alternately positive and negative. Accordingly the intensities, 

 1 + m, 1 + m-m', 1 + m - m' + m x/ , &c., are alternately greater 

 and less than 2 ; and the intensity of the light sent to the 

 point E is alternately greater and less than when no obstacle 

 is interposed. 



It will be easily understood, from this general explanation, 

 in what manner the magnitude of the fringes depends on the 

 length of the wave, on the distance of the luminous origin 

 from the obstacle, and on the distance of the screen. They 

 must be broadest in red light, and narrowest in violet light ; 

 and in white or compound light, the diffracted bands of dif- 

 ferent colours will occupy different positions, so as to form a 

 succession of iris-coloured bands having the violet or blue in- 

 side, and the red without. After a few successions these 

 bands wholly disappear, owing to the superposition of bands 

 of different colours. 



(126) It is easy to compute the relative places of the 

 same fringe, for different positions of the luminous point, and 

 of the screen. 



Let P be the edge of 

 the obstacle, PA a por- 

 tion of the wave, diverg- 

 ing from 0, which has 

 just reached that edge ; 

 and let QR be the screen, and R the place of a fringe of any 



