( 839 } 



XLI. — On a Table of Numerical- Apertures, showing! the Equivalent 

 Angles of Aperture of Dry, Water Immersion, and Homogeneous 

 Immersion Objectives, with their respective Resolving Powers, 

 taking the Wave Length of Line Eas the Basis ; a = n sin. to, 

 n = refractive ificlex, and tv = ^ angle of aperture. 

 By J. W. Stephenson, F.R.A.S., Treas. E.M.S. 



(Bead 12th Nov., 1879.) 

 As considerable misapprehension appears to exist, not only in this 

 country but also in the United States, as to the special advantage 

 of the " Numerical-Aperture " of Professor Abbe, I have thought it 

 would be useful to construct the subjoined Table. It cannot be 

 too strongly impressed upon microscopists, that the expression 

 angle of aperture of objectives furnishes in itself no intelligible 

 measure of the actual resolving powers, which, as will be seen by 

 the Table, bear no relation whatever to the angles. 



The resolving powers are, however, exactly proportional (cseteris 

 paribus) to the numerical apertures, and the expressions for the 

 latter will therefore allow the resolving powers of different objec- 

 tives to be at once compared, not only if the medium (air, water, 

 oil, &c.) is the same in each case, but also if it is different. 



Thus, to say that a dry objective has an angle of 60'^, a water- 

 immersion 53°, and a homogeneous immersion 48°, conveys no 

 idea (without calculation) of their relative resolving powers, but 

 when we are told that the three objectives are of • 50, " 60, and 

 • 62 numerical aperture, the comparison is obvious. 



The Table shows, moreover, how little increase in resolving 

 power may be gained by a considerable increase in the angle. 

 Thus two dry objectives whose angles are 180° and 157° respec- 

 tively, differ in resolving power by only 2 per cent. 



Maximum aperture of 

 homogeneous immer- 

 sion objectives, with 

 crown-Klass cover . . 



Zeiss' homogeneous |th~ 

 (1879) , 



Water 



Angle. 



Theoretical 

 Resolving 



J'ower, 



in Lines to 



an Inch. 



(A.=0- 5269/01 



line K.) 



180° 

 161° 

 153° 

 147° 

 142° 

 138° 

 134° 

 13U° 

 126° 



123° 40' 



146,528 

 144,600 

 142,672 

 140,744 

 138.816 

 136,888 

 134,960 

 133,032 

 131,104 

 129,176 



