62 NOTES ON MICROSCOPICAL OPTICS: 



in the blue and violet end and undercorrect it in the orange and 

 red end. As the crown lenses alone would bring violet to a shortest 

 and red to a longest focus, the effect is that the achromatic com- 

 bination brings both ends of the spectrum to a longer focus than 

 its central part. Therefore there is a minimum distance of the focus 

 for yellow-green, and at that focus the light from both ends of the 

 spectrum is diffused, and causes a halo of a purple or claret tint. 

 This halo is objectionable even in visual observations, because it 

 falsifies the true colour of the observed objects, but the difference 

 of focus to which it is due becomes a grave defect when the object 

 is to be photographed, unless a strong screen is used which cuts off 

 both ends of the spectrum, but more particularly the dark blue and 

 violet light. Such a screen greatly increases the required time of 

 exposure, and may be inadmissible in the case of stained or naturally 

 strongly coloured objects, because these may be either opaque or too 

 transparent to yellow-green light. 



The attempts to produce varieties of glass free from this secondary 

 spectrum have been unsuccessful as far as the microscope is con- 

 cerned, 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 whose value for this pur- 

 pose 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 objectives, 

 and fluorite of good optical quality must be used to this day to 

 secure the result. Apart from the difficulty of finding this material 

 there is no obstacle to the designing by exact calculation of apo- 

 chromatic objectives. 



I now coniie to a defect of nearly all microscope objectives, and 

 especially of highly corrected ones, which is well known to all prac- 

 tical microscopists, namely the pronounced curvature of the field, 

 invariably 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 aberra- 

 tions 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 undercorrected 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 overcorrected astigmatism 

 must be regarded as the ideal in microscope objectives. Unfortunately 

 this desirable state cannot be reached in the existing types of 

 objectives. The binary low power objectives up to the ordinary one 

 inch and 2/3 inch come nearest to it, and are therefore justly liked 



