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XIV. On ' An Optical Paradox.' 

 By G. Johnstone Stone y, M.A., Sc.D., F.R.S* 



IN the June number of the Phil. Mag. vol. ix. p. 779, 

 Lord Rayleigh describes and discusses an experiment 

 by which he was at first puzzled. The experiment is illus- 

 trated by a diagram, which is here reproduced. 



A is a point-source of light of nearly wave-length \, L is 

 a lens forming an image of A upon the middle of C, which 

 last is the objective of a telescope T. The telescope is to be 

 f ocussed upon lens L ; and the boundary of this lens is then 

 the object which will be more or less satisfactorily seen by 

 an observer who looks through the eyepiece of the telescope. 

 The excellent definition of L as seen in the telescope was 

 unexpected. It would seem paradoxical to a person who, 

 remembering that most of the light from A is concentrated 

 within the minute " spurious disk " of its image formed at C, 

 was disposed at first to infer that this little disk may be 

 regarded as determining the effective aperture of telescope T. 



Lord Rayleigh interposed a material screen cutting down 

 the aperture of the telescope to nearly the above small size. 

 This greatly impaired the image of L as seen through the 

 telescope ; and this satisfied him that the effective aperture 

 of the telescope before the interposition of the screen was 

 not so small as had been supposed. Lord Rayleigh was led 

 by this to make a closer theoretical discussion of the pheno- 

 menon, and obtained the definite integral upon which the 

 question turns. 



Lord Rayleigh also considers the effect of enlarging A, 

 the source of light ; and expresses the opinion that if the 

 enlarged source is a self-luminous body, there will be " no 

 possibility of bringing into play the interferences upon which 

 the advantage of a large aperture depends," inasmuch as 

 with a self-luminous source of light it was supposed that there 

 can be " no phase-relation between the lights which act at 

 different parts of the object-glass.'''' This view, as it appears 

 to the present writer, is based upon an oversight. The in- 

 terferences upon which resolution depends are of quite 

 another kind as will be explained in a subsequent paragraph, 



* Communicated by the Author. 



