COLLAR CORRECTION FOCI OF LENSES 21 



An aplanatlc objective can be made into an under-corrected 

 objective by (1) causing the back lenses of ivhich it is composed 

 to approach the front lens. This is the device of Andrew Ross, and 

 is now effected l by means of a special ' collar ' arrangement, which, 

 by the action of a screw, approximates or separates the suitable 

 lenses. But for this a special device is needed for each objective. 

 (2) The result can moreover be secured by causing the eye-piece to 

 approach the objective,. This of course is accomplished by the use of 

 the draw-tube, and must be employed with objectives having rigid 

 mounts. 



Closing lenses, that is, bringing them together, whether in the 

 objective itself or in the microscope as a whole, by shortening the 

 distance between the eye-piece and the objective, under -corrects the 

 objective, that is, gives negative aberration ; while the separation of 

 lenses over-corrects or gives positive aberration. 



In using the collar correction l for a longer body or a thicker 

 cover-glass the collar adjustment must be moved so as to cause the 

 back lenses of the objective to approach the front lens, while for a 

 shorter body or a thinner cover-glass, the adjustment must be moved 

 so as to cause their separation. 



In correcting by tube length for a thicker cover shorten the tube, 

 and for a thinner one lengthen it. 



For the benefit of those who aim at work with lenses, that is 

 such as may be compassed with the aid of the most elementary 

 mathematics, it may be well to indicate a simple method for the 

 deduction of the foci of plano-convex and biconvex lenses. 



In fig. 17 the focus is twice the radius measured from the vertex 

 A, that is, A F. But in fig. 18 it is twice the radius measured 

 from the point A, that is, the point 

 F is distant from the lens twice the 

 radius less two-thirds the thickness 

 of the lens. 



Similarly, in fig. 25, the focus 

 of a biconvex lens is measured from 

 the point A ; in other words, F is 

 distant from the lens the length of 

 the radius less one-sixth the thick- FIG. 25. The focus of a convex lens 

 ness of that lens (nearly). 



Formula relating to a biconvex lens. Where P is one focus, P r its 

 conjugate, F principal focus (solar focus, or that for a very distant 

 object), R radius of curvature for one surface, R' for the other 

 surface, p the refractive index of the medium, then 



1 1 



FIG. 25A. Focus of a concave lens. 

 1 See Chapter V. 



