20 



CONSTRUCTION OF THE MICROSCOPE. 



fig. 13. 



vex, provided the distance of the point of convergence or divergence 

 from the centre of the first surface is to the radius of the first surface 



as the index of refraction 

 is to unity. Thus, if m I 

 I n is a meniscus, and r I, 

 r I' rays converging to the 

 point e, whose distance 

 e c from the centre of the 

 first surface I a I' of the 

 meniscus is to the radius 

 c a, or c I, as the index 

 of refraction is to unity, 

 that is as 1-500 to 1 in 

 glass; then if /is the fo- 

 cus of the first surface, 

 describe, with any radius 



less than fa, a circle ma' n for the second surface of the lens. Now it 

 will be found by projection, that the rays r I, r I', whether near the axis 

 ae or remote from it, will be refracted accurately to the focus/- and as 

 all these rays fall perpendicularly on the second surface m n, they will 

 still pass on, without refraction, to the focus/ In like manner, it is 

 obvious that rays fl, fl' } diverging from / will be refracted into r I, r I', 

 which diverge accurately from the virtual focus.* ** 



There are certain mechanical difficulties in the way of such lenses 

 as these, but which have to some extent been surmounted by dimin- 

 ishing the working aperture with stops, for correcting their aberra- 

 tion. This is still better effected, or even got rid of altogether, by 

 using combinations of lenses, so disposed that their opposite aber- 

 rations shall correct each other, whilst magnifying power is gained. 

 For it is easily seen that, as the aberration of a concave lens is just 

 the opposite of that of a convex lens, the aberration of a 

 convex lens placed in its most favourable position may be 

 corrected by a concave lens of much less power in its most 

 favourable position. This is the principle of a combina- 

 tion proposed by Sir John F. W. Herschel, fig. 14, con- 

 sisting of a plano-convex lens and a meniscus ; and a 

 doublet of this kind will be found extremely useful and 

 available for microscopic purposes : it affords a large field, 

 like the Coddington lens. Another and serious difficulty 

 arises to the optician in the unequal refrangibility of the different 

 coloured rays which together make up white light, so that they are not 

 * Brewster's Optics. 



fig. 14. 



