LIMIT OF RESOLUTION 



315 



light, will be examined first. As the beam of light passes through the 

 slit it spreads out to a certain extent, producing a fuzzy -edged outline 

 caused by the diffracted light which spreads into the geometrical shadow. 

 If the geometrical pattern is focused on a photographic plate by means 

 of a lens it will be found that the developed photographic image is 



I_ 



'22 



J! i 



22 



22 



V 



22 



Fig. VIII-3. A photometric analysis of the Fraunhofer diffraction patterns of 

 two identical sources. The distance of nearest approach d has been reached where 

 I is still distinguishable from /'. The intensity of the secondary maximum is not 

 shown. It is 7/62. 



edged with a series of dark and bright diffraction bands. The intensity 

 distribution I across such a photographed slit is shown as a broken 

 line in Fig. VIII-3, provided that the exposure is not too long to bring 

 out the diffraction bands of lower intensity than the first. Note that 

 the intensity I at the center of the slit rapidly drops to zero at the dis- 

 tance d and then passes through a secondary maximum of intensity J/22 

 which is the first diffraction fringe. 



If two such slits separated by a distance d are simultaneously photo- 

 graphed, the two image patterns I and l' will overlap as shown in 

 Fig. VIII-3. 



The distance d between the maxima of these two diffraction patterns is 

 the measure of the resolution. 



The limit of resolution is defined by the distance d of nearest approach 

 of two sources emitting monochromatic light such that, in the maximum 

 intensity curves, the foot of one and the maximum of the other coincide. 



Whereas a single slit aperture forms a series of fine dark and bright 

 bands, a square aperture forms bright and dark bands in two directions 

 crossing each other at right angles. If the aperture is circular the 

 pattern is in the form of a central bright disk surrounded by bright rings 

 rapidly decreasing in intensity. 



The mathematical analysis of the angular separation of the diffraction 

 circles is a problem of considerable mathematical difficulty. The angu- 



