548 



NATURE 



[January 22, 1920 



with microscopes under ordinary conditions if we 

 want to get the best optical effect. We may, as a 

 matter of convenience, have still higher magnifica- 

 tions, because it is not given to everybody to appreciate 

 fine detail unless an image is somewhat enlarged. But 

 it must be appreciated that any increase beyond 750 or 

 .Soo diameters does not result in our seeing anything 

 more. It simply allows us to see the object on a 

 somewhat larger scale. We may, therefore, sum- 

 marise as follows : An object which is much smaller 

 in size than the resolution limit can be rendered 

 visible provided the light with which it is illuminated 

 is of sufficient intensity and sufficiently different in 

 refractive index from the medium in which it lies. 

 To resolve a series of equidistant points or lines in 

 an object, their distance apart must exceed half a 

 wave-length of light in the medium in which the 

 object is immersed. Johnstone Stoney has shown that 

 a pair of lines or objects can be separated when their 

 distance apart is rather smaller than the resolution 

 limit required for a number of points or lines in a 

 row. But it should be borne in mind even here that 

 the resolution limits apply if a clear standard of 

 definition is required. An isolated object or pair of 

 objects are not so well defined if they exceed the 

 resolution limits as laid down for recurring structures. 

 It cannot be too fully appreciated that illumination is 

 the keynote of all sound microscopic work, and this 

 applies whether the illumination is by means of visible 

 radiation under ordinary conditions of work, or 

 whether it is in experimental work in which the use 

 of invisible radiations are concerned. 



There is much room for research in this direction, 

 and it is to be hoped that this is one of the points 

 which will be seriously taken up. Apart from any 

 question of research, 'the education of the user is 

 perhaps of vital importance. It is of little use for 

 opticians to make great efforts to turn out a satis- 

 factory instrument if the user is incapable of taking 

 advantage of the quality of the optical or other parts. 

 I trust, therefore, that this symposium will give an 

 impetus in this direction, and that it will help 

 microscope-users to realise how much remains to be 

 done. 



I 



MICROSCOPICAL OPTICS.^ 



N the opening paragraphs attention is directed to 

 the methods of treating the aberrations on the 

 principle of equal optical paths (A. E. C, Monthly 

 Notices of R.A.S., January and March, 1904, and 

 April, 1905) and to the author's recent determination 

 of the actual light distribution at and near the focus in 

 the presence of aberration (Monthly Notices, June, 

 igig). The sine-condition is also discussed. 



The origin and effects of the secondary spectrum 

 are then dealt with, and the paper proceeds : 



The attempts to produce varieties of glass free from 

 this secondary spectrum have been unsuccessful so far 

 as the microscope is concerned, for the existing crowns 

 and flints with proportional dispersion have so little 

 difference in dispersive power that an impracticable 

 number of lenses would have to be used to secure the 

 desired effect. We therefore still depend on the 

 material the value of which for this purpose was 

 discovered by Abbe, the natural mineral fluorite, used 

 instead of crown glass in combination with heavy 

 crown glasses or very light flint glasses in place of 

 ordinary dense flint glass. It was by the use of 

 fluorite that Abbe produced the apochromatic objec- 

 tives, and fluorite of good optical quality must be used 

 to this day to secure the result. Apart from the 



1 From a paper by Prof. A. E, Conrady presented at a discussion on 

 "The Microscope : Its Design, Construction, and Applications," organised 

 by the Faraday Society at the Royal Society on January 14. 



NO. 2621, VOL. 104] 



difficulty of finding this material, there is no obstacle 

 to the designing by exact calculation of apochromatic 

 objectives. 



1 now come to a defect of nearly all microscope 

 objectives, and especially of highly corrected ones, 

 which is well known to all practical microscopists, 

 namely, the pronounced curvature of the field, in- 

 variably in the sense of requiring a shortening of the 

 distance from object to lens in order to obtain a sharp 

 focus in the outer parts of the field of view. The 

 general theory of the primary aberrations of oblique 

 pencils shows that any lens system when freed from 

 astigmatism will have the curvature of field defined 

 by the Petzval theorem, and that in the presence of 

 astigmatism the two focal lines which then represent 

 the strongest concentration of the light always lie 

 both on the same side of the Petzval curve and at 

 distances from it which are in the approximate ratio 

 of three to one. When the astigmatism is under- 

 corrected the natural curvature of the field defined by 

 the Petzval equation becomes aggravated, whilst over- 

 corrected astigmatism tends to flatten the field, and is 

 deliberately introduced for this purpose in ordinary 

 photographic objectives. The presence of considerable 

 amounts of astigmatism, of course, renders really sharp 

 marginal images impossible in either case, so that 

 its absence, or, better still, a modest amount of over- 

 corrected astigmatism, must be regarded as the idtal 

 in microscope objectives. Unfortunately, this desir- 

 able state cannot be reached in the existing types of 

 objectives. The binary low-power objectives up to the 

 ordinary i in. and f in. come nearest to it, and are, 

 therefore, justly liked by microscopists for all work 

 for which they are sufficiently powerful. In the 

 ordinary ternary objectives of the ^-in. type, with ap- 

 proximately plano-convex components, the curvature 

 of the field is also of reasonably moderate amount. 

 But it is a general experience that highly corrected 

 objectives are very much worse as regards curvature 

 of field. In the light of my most recent work on the 

 general theory of lenses (Monthly Notices, November, 

 1919), this curious and objectionable peculiarity is 

 easily explained, and becomes revealed as a necessary 

 consequence of high spherical and chromatic correc- 

 tion if the usual number of components is adhered to. 

 In the Lister and Amici types of ordinary objectives, 

 which are fairlv satisfactory as regards curvature of 

 the field, the front lens is of such a form as to 

 produce strong outward coma, and there is in the back 

 lens»or lenses a corresponding amount of inward coma. 



The simple extensions of Seidel's theory, given in 

 the paper last referred to, show that this is the state 

 of affairs which tends to diminish undercorrected 

 astigmatism, or even to reverse it into the more desir- 

 able overcorrected form. High correction of the zonal 

 spherical aberration, and to a still greater extent corn- 

 plete removal of the spherical variation of chromatic 

 correction, necessitate a more or less complete reversal 

 of the coma effects in front and back components. In 

 other words, with the usual types of objectives reduc- 

 tions of curvature and apochromatic or serni-apo- 

 chromatic correction are completely antagonistic and 

 incompatible; what benefits one correction is detri- 

 mental to the other. Fortunately, the extended theory 

 also indicates a way out of this dilemma. It appears 

 fairlv certain that by building the objective itself on 

 the lines required by the apochromatic condition, but 

 leaving it spherically undercorrected, perhaps also 

 chromatically overcorrected to a moderate extent, and 

 with a considerable amount of outward coma (this is 

 the most important), and by correcting these residuals 

 in a widely separated additional back lens, it will be 

 possible to' combine moderate curvature of field with 

 apochromatic perfection, and thus to remove the worst 

 outstanding defect of the best objectives. 



