DIFFRACTION. 117 



AB = b, and AP =r ; then, since r is very small in compari- 

 son with a and , it is easy to see that 



Now when this interval is equal to a whole number, n, of 

 semi- undulations, the aperture may be divided by concentric 

 circles, such that the rays which reach the point B, coming 

 from any two successive circumferences, shall differ by the in- 

 terval of half a wave. It follows from the preceding for- 

 mula that the squares of the radii, and therefore the superficies 

 of the successive circles thus formed, are as the numbers 

 of the natural series ; so that the annuli comprised between 

 every two succeeding circumferences are equal. But the ele- 

 mentary waves proceeding from each annulus are in complete 

 discordance with those from the two adjacent. The successive 

 annuli will therefore destroy one another's effects, and the 

 total intensity of the light at the point B will be null, or 

 equal to that of the last, according as the number of an- 

 nuli (the central circle included) is even or odd. Hence, 

 for a given aperture there will be a succession of points on 

 the axis, at which the intensity of the light is alternately 

 nothing and a maximum ; and it is obvious from the preceding 

 that the distances of these points will be the values of b given 

 by the formula 



in which the points of complete darkness correspond to the^ 

 even values of n, and those of maximum brightness to the 

 odd values. 



Such is the case with homogeneous light. As the points 

 of maximum and minimum intensity are different for the rays 

 of different colours, there will be no point of complete dark- 





IT7 



