Professor Alfred W, Porter, D.Sc, F.R S., spoke on 

 *' The Resolving Power of Microscopes." 



NOTES ON THE RESOLVING POWER OF MICROSCOPES. 

 By Alfred W. Porter, D.Sc, F.R.S. 



The question of resolving power was first of all discussed in con- 

 nection with telescopes; but the problem for microscopes is essen- 

 tially identical with that for telescopes. The fact that telescopes 

 of large aperture gave smaller star-images than those with small 

 aperture was first demonstrated by W. Herschel (1805) and later by 

 Foucault (1858). The explanation was given in terms of the wave 

 theory of light by Fraunhofer (1823) and by Airy (1834). Owing 

 to the wave structure of light, each image of a luminous point 

 formed by a lens is found (both experimentally and by the wave 

 theory as developed by Fresnel) to be a circular bright disc sur- 

 rounded by dark and bright rings of intensity diminishing outwards. 

 If there are two bright sources sufficiently close — two stars, for 

 example — their individual discs may overlap; and for a certain 

 degree of closeness the confusion is so considerable that it is im- 

 possible to detect the double nature of the source. 



Some convention had to be adopted in specifying the limit at 

 which separation between the discs can be appreciated. The con- 

 vention actually adopted has been based on the fact that if the 

 centre of the image of one star falls on the first dark ring of the 

 other, then the brightest part of the combined image will be a 

 figure-of-eight disc having a faint diminution of intensity at its 

 middle, which reveals its composite character. Now the radius of 

 the first dark ring (as calculated by Fraunhofer) is 



1.22 XF 

 B 

 where B is the diameter of the object-glass and X the wave-length 

 of the light received. The angular separation of the stars when 

 just resolved (according to the convention) is obtained (in radians) 

 by dividing this by the focal length of the lens. The reciprocal of 

 this is the angular resolving power. Practice has shown (Dawes; 

 E. M. Nelson) that resolution is obtained when the sources are 

 more than 25 per cent, closer than this. It was shown theoretic- 

 ally by A. W. Porter (R. Micr. J., 1908, Part I.) that the true 

 limit (for which there would be no diminution in intensity at the 

 middle of the double image) corresponds to a closeness of the stars 

 for which the intensity curves would cross at their points of inflexion ; 

 this limit corresponds very nearly to that obtained from observation. 



The question of resolving power is not, however, an exact branch 

 of science. It is the *' thing seen '"' with which we are concerned, 

 and this depends upon who sees. The human element enters ; and 



