Tlie Relation of Aperture and Power. By Prof. E. Ahhe. 801 



Other defects arise from the disproportionate increase of the 

 dispersion from the red to the blue, which is found in all kinds of 

 optical glass hitherto produced, and forbids a really perfect 

 chromatic correction of the systems. In regard to all of these 

 aberrations it may be readily shown that they must introduce 

 greater and greater uncorrected residuals as the numerical aperture 

 of the cone of collected rays is more and more increased, other 

 circumstances being equal.* 



It is therefore obvious that under equal conditions of technical 

 construction the inherent dissipation of the light will always be 

 greater with the wider apertures, and consequently the super- 

 amplification which is compatible with any given degree of 

 precision of the image will be confined to a loiver figure with 

 objectives of wide than with objectives of low aperture, which 

 inference is fully justified by experience.! 



(h) On the other hand, theory indicates different conditions for 

 the residuary aberrations, with even the same (numerical) apertures, 

 when objectives of different systems^dry and immersion — are com- 

 pared. The uncorrectable residuals of the aberrations will always 

 be greater when the total amount of aberrations requiring correc- 

 tion is greater. Now the front-aberration, which is a very pre- 

 dominant part of the total amount in dry lenses of somewhat wide 

 aperture, is considerably diminished with water-immersion and 

 almost entirely suppressed by the homogeneous-immersion system. 

 We expect therefore a higher value of admissible super-amplifica- 

 tion in the case of homogeneous immersion than in that of water- 

 immersion; and a still higher for water-immersion than for dry — 

 provided always that objectives of the same (numerical) aperture 

 are compared ; and conversely, one and the same super-amplification 



* That the numerical aperture is the essential element and not the aperture- 

 angle, results from the fact that all the effects considered above depend on the 

 proportion of the clear aperture to the focal length of the objective, which pro- 

 portion is exactly expressed by the numerical aperture. 



t The above statement does not of course imply the opinion, that an objective 

 of lower aperture should, under all circumstances, admit of a higlier super- 

 amplification practically than one of wider aperture. The " definition " of a lens, 

 in the generally adopted sense, is quite another thing to the dioptrical precision 

 of the image, which is in question here. There may be lack of " delineating 

 power " when a certain amplification is reached, and then every increase of the 

 amplification renders the impression of the image worse and worse, notwithstanding 

 the utmost perfecticm of the dioptrical performance of the lens. If, for instance, 

 an objective of O'l N.A. were made with the short focal length of a l-8th, it would 

 not bear even the lowest eye-piece, because the normal power of the system 

 (80 diameters) is already an empty power for so narrow an aperture, whilst a 

 well-made l-8th of O'S N.A. will give a satisfactory image with a relatively 

 strong ocular. If, however, an objective of " 1 iST.A. has a focal length of say 

 1 inch, it will bear a deeper eye-piece than a l-8th of ' 8 without any perceptible 

 loss of sharpness. In order to compare microscopic images in regard to their 

 dioptrical conditions, the strange element of " lack of definition of empty powers " 

 must be excluded. 



