[ 673 ] 



LXXVII. On the Formation of Images by means of an 

 Opaque Disk. By Alfred W. Porter, F.R.S., Uni- 

 versity College, London *. 



[Plate IX.] 



IN spite of the prominence given in treatises on Physical 

 Optics to the existence of the bright spot at the centre 

 of the shadow formed by a point-source and a circular disk, 

 it does not seem to have been recognized that, as ordinarily 

 exhibited, the bright spot is in reality an image of the source 

 of light. The source is never a point-source in practice, and 

 the contour of the bright patch is simply the locus of the 

 diffraction spots formed by the various points on the contour 

 of the source of light. I have for some years been impressed 

 by the very sharp boundary of the bright spot when obtained 

 by means of a pinhole source ; a sharpness quite inconsistent 

 with one's expectations from the account usually given. 

 It was only a few weeks ago that it occurred to me that the 

 explanation is that the theoretical bright spot is much smaller 

 than the patch of light obtained. To test this I took in the first 

 place a circular source about 9 mm. in diameter, with a thin 

 wire stretched across its centre, illuminated from behind by 

 an electric arc, and found as I suspected that the spot was 

 transformed into a sharp image of the bright opening with 

 its dark bar. We have thus the possibility of obtaining 

 sharp images of small objects, using an opaque disk instead of 

 a lens. In conjunction with Mr. E. Talbot Paris, I have 

 taken photographs of a triangular opening ; one of: these is 

 reproduced (PI. IX.). 



The size of the true bright spot is easily obtained 

 theoretically for a source on the axis of the disk. 



The intensity at any point Q distant r from the axis is 



given by (Vr + V 2 ) 



1_ (a + by ' 



z c 3 



where Vj= - Ji(c)— -. ^ J z (z) + etc., 



V = J (c)-^J 2 (;)+ etc., 



_ 2>n-(a + b)i 



abX 



y 



and 



ZTTVC 



Xb 



The maxima and minima are given by V Jj = 0. The 

 * Communicated by the Author. 



