%22 H - SAGAOKA; DIFFRACTION PHEXOMEX 



simplest case involves complicated mathematical analysis, so that the 

 result arrived at is only an approximation barely sufficient for 

 practical purposes. 



In the present paper, I give, in the first place, a general 

 discussion of the Fraunhofers diffraction phenomena of a circular 

 aperture for a finite source of light. I then pass on to the considera- 

 tion of the intensity of illumination both inside and outside a circulai- 

 image, and show how, by the superposition of two systems of lines 

 of equal intensity, we can explain the formation of a ligament 

 during the ingress or egress of a dark disc over a luminous edge, as 

 verified by the experiments of André and Angot.* 



§ 1. General Expression for the Intensity. 



It is well-known that the circular aperture of a telescope gives rise 

 to a diffraction pattern, consisting of concentric rings with luminous 

 centre, when the source of light is a point, If instead of a luminous 

 point, we have a finite source of light, each of its elements will 

 produce similar phenomena ; so that the illumination In the focal plane 

 of the telescope becomes the integral effect of all the points of light 

 within a given geometrical area. Even with a uniform source, the 

 intensity of the image is not uniform but, as is seen in the focal plane 

 of the telescope, is distributed according to a law depending on the 

 shape of the source and the size of the aperture. 



Let the circular opening of the telescope be taken for the xy plane; 

 denote the cosines of the angles which the incident ray makes with the 

 x and y axes by a and ß, and those for the diffracted ray by a and ß'. 

 Putting E=radius of the telescope aperture, A = wave length of light, 

 ,. = 27Ty/(a-a ) 2 + (ß-ß'? Bi we j aiow t \ lilt the intensity of the diffracted 



A 



light in the focal plane of the telescope is proportional to 



André et Angot, Annales de l'École Normale, 10. 323. 1881. 



