406 



Transactions of the Society. 



The Law of Diffraction for Focussed Light. 



We thus see that the course of diffracted light through an 

 optical instrument can be traced and the focal points of diffracted 

 beams can be found without any detailed consideration of the 

 refractive systems employed and so we can arrive at the important 

 generalisation that the diffraction pattern produced by any given 

 aperture in the focal plane of a lens or system of lenses is simply 

 the focussed image of the diffraction pattern which without that 

 lens the same aperture would throw upon the same plane. We 

 thus arrive at the enormous simplification of being able to make 

 all our calculations relating to diffraction in the open air. 



It will be evident that the foregoing proof does not depend 



Fig. 03. 



upon the assumption of any particular magnitude for the diver- 

 gence angle at the point e. If instead of the diverging beam 

 which passes the aperture A. . . A (fig. 91) we had assumed a beam 

 of parallel light coming from infinite distance, and the focal plane 

 I?...?/! to be the principal focal plane of the system, the proof 

 would have been just the same. Take then the following case, 

 illustrated by fig. 93. Here e lies in the principal focal plane of 

 a lens filling the aperture Ai and ?? lies in the principal focal plane 

 of another lens filling the aperture A 2 . They are therefore con- 

 jugate points and images one of the other, and the beam which 

 Dasses between them passes from Ai to A a in the form of plane 

 wave-fronts or parallel rays. In this region between the two 



