Notes. 417 



An Optical Paradox* 

 By Lord Rayleigh, O.M., F.R.S. 



Consider the following combination : — A point source A of 

 approximately homogeneous light (A,) is focused by the lens LL 

 upon the object-glass of a telescope T. In its turn the telescope 

 is focused upon L. According to geometrical optics the margin 

 of the lens L should be seen sharp by an eye applied to the 

 telescope ; but when we consider the limitation of aperture at the 

 object-glass of the telescope, we come to the conclusion that the 

 definition must be very bad. The image of A at C constitutes 

 the usual diffraction pattern of which most of the light is concen- 

 trated in the central disc. The diameter of this disc is of the order 

 X.LC/LL. If this be regarded as the effective aperture of T, the 

 angular resolving power will be found by dividing X by the above 



Fig. 83. 



quantity, giving LL/LC; so that the entire angular magnitude of 

 the lens LL is on the limits of resolving power. 



If this be admitted, we may consider next the effect of en- 

 larging the source A, hitherto supposed to be infinitely small. If 

 the process be carried far enough, the object-glass of T will become 

 filled with light, and we may expect the natural resolving power 

 to be recovered. But here we must distinguish. If the enlarged 

 source at A be a self-luminous body, such as a piece of white-hot 

 metal or the carbon of an electric arc, no such conclusion will 

 follow. There is no phase-relation between the lights which act at 

 different parts of the object-glass, and therefore no possibility of 

 bringing into play the interferences upon which the advantage of a 

 large aperture depends. It appears, therefore, that however large 

 the self-luminous source at A may be, the definition is not im- 

 proved, but remains at the miserably low level already specified. 

 If, however, the source at A be not a real one, but merely an 

 aperture through which light from real sources passes, the case 

 may be altered. 



Returning to the extended self-luminous source, we see that the 

 inefficiency depends upon the action of the lens L. If the glass 



* Reprinted by permission of the author from Phil. Mag., June 190.5, pp. 779-81. 

 Aug. 16th, 1905 2 F 



