344 H - NAGAOKA ; DIFFEACTIOX PHENOMENA 



of which the right side applies to jj (inside the circle) and that to the 

 left to I e (external to the circle). 



Having found the values of these different integrals, we are now 

 in a position to discuss the illumination near the rim of the circular 

 image. 



We have already found that the intensity of light at the centre of 

 a circular disc is nearly equal to unity when the diameter is tolerably 

 large, and at the rim nearly equal to half the intensity at the centre. 

 As will be seen from the expression for Z t , the intensity increases very 

 rapidly from the rim towards the centre, and from that for J e , decreases 

 very rapidly as we pass from the rim outwards. In fact the variation 

 of intensity is greatest near the rim, the change however not taking- 

 place abruptly but fading away gradually, as illustrated in Fig. 6 

 PI. XVII, in which the dark line refers to « = co and the dotted line to 

 a = 40. The image of a luminous disc as seen through a telescope is 

 thus not sharply denned, as the intensity at the geometrical rim 

 changes continuously. If the intensity for the limit of visibility 

 be less than I R , the image of the disc will appear to a slight extent 

 broadened. 



§7. Lines of Equal Intensity. 



For practical purposes, it is sometimes convenient to draw the 

 lines of equal intensity. For a circular disc, they consist of a series 

 of concentric circles, which drawn for equal differences of intensity 

 crowd together near the geometrical edge. When there are different 

 sources of light, we can superpose the separate effects and graphically 

 represent the distribution of intensity in the following manner. 



Draw the lines of equal intensity for the image of each source, and 

 at the point of intersection of any two lines, the intensity will be the sum 

 of the two. We thus obtain a system of points of equal intensity. By 



