1 6 ELEMENTARY PRINCIPLES .OF MICROSCOPICAL OPTICS 



grasp of them, to draw such a lens, and trace the paths of two rays 

 through it, one near the axis, the other near the edge ; then do the 

 same with the lens reversed. 



Formula for spherical aberration : 1 



f If lr> f r' f r' 



where f = principal focal length ; y = semi -aperture ; p = refr. 

 index ; and r, r', radii. 



Q 



In an equi-convex of crown, where p = , r = r' = /, 



sf- - 5 . >>* 

 f 3 / 



o / 



In a plano-convex of crown, where /z = -, r' = oo, r = '-, 



7 ?/ 2 

 I f = - ~ . Here parallel rays are incident on the convex 



6 / 

 surface. But when parallel rays are incident on the plane surface, 



H = , r = co, r' = -, $f= ' ; consequently the sphe- 



Z JL 2 j 



rical aberration is four times as great (see figs. 17 and 18). 



When r' oo, and p = 1'69, the plano-convex becomes the 

 form of minimum aberration. 



q 



In a crossed 2 biconvex lens, where r f = 6 r, and p = , 



15 ?/ 2 

 Sf= ; - f1 the parallel rays being incident on the more 



curved surface. 



Formula for finding the principal focus F of a lens equivalent to 

 two other lenses whose foci are f, f and their distance apart d : 

 1 __ 1 J__ _c_ 



F""/V ff 1 ' 



In figs. 5, 8, and 9 we see that when the incident ray D E con- 

 sists of white light, the colours of which it is composed are unequally 

 refracted ; the two extremes, R (red light) and Y (violet light), being 

 bent in different directions, the other colours lying between them 

 in their proper order. 



This unequal refraction of the different colours takes place in 

 like manner in spherical lenses, and it is then known as chromatic 

 aberration. 



The effect of this upon the action of a lens is that, if parallel white 

 light fall upon a convex surface, the most refrangible of its component 

 rays (which, as we have seen, is the violet) will be brought to a focus 

 at a point somewhat nearer the lens than the principal focus ; and 

 the red ray, having the least refrangibility, will be brought to a focus 

 at a point farther from the lens than its principal focus, which is, in 

 effect, the mean of the chromatic foci. 



1 Encyclopedia Brit. vol. xvii. 



2 A biconvex lens is said to be ' crossed ' when the radii of its surfaces are in the 

 proportion of 1 : 6. 



