780 An Optical Paradox. 



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

 of bringing into play; the interferences upon which the ad- 

 vantage of a large aperture depends. It appears, therefore, 

 that however large the self-luminous source at A may be, the 

 definition is not improved, 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 be removed from its seat, so that A is no longer 

 focused upon the object-glass, the definition must recover. 



I do not know how far the above reasoning will seem 

 plausible to the reader, but I may confess that I was at first 

 puzzled by it. I doubt whether any experimenter would 

 willingly accept the suggested conclusion, though he might 

 be unable to point out a weak place in the argument. He 

 would probably wish to try the experiment; and this is easily 

 done. The lens L may be the collimating-lens of an ordinary 

 spectroscope whose slit is backed by a flame. The telescope 

 is removed from its usual place to a distance of say 10 feet 

 and is focused upon L. The slit is at the same time focused 

 upon the object-glass of the telescope. Although the image 

 of the slit is very narrow, the definition of L as seen in the 

 telescope does not appear to suffer, the vertical parts of the 

 circular edge (parallel to the slit) being as well defined as the 

 horizontal parts. If, however, at the object-glass a material 

 screen be interposed provided with a slit through which the 

 image of the first slit can pass, the definition at the expected 

 places falls off greatly, even although a considerable margin 

 be allowed in the width of the second slit. 



This experiment gives the clue to the weak place in the 

 theoretical argument. It is true that the greater part of the 

 light ultimately reaching the eye passes through a very small 

 area of the object-glass ; but it does not follow that the re- 

 mainder may be blocked out without prejudice to the definition 

 of the boundary of the field. In fact, a closer theoretical dis- 

 cussion of the diffraction phenomena leads to conclusions in 

 harmony with experiment. 



In the case of a point-source and the complete circular 

 aperture LL, the question turns upon the integral 



f 



Jo 



J (a#) Ji(fix)(Lv, 



J , Jj being the Bessel's functions usually so denoted. The 



