SPHERICAL ABERRATION 15 



light parallel to the axis falling on a plano-convex lens of crown 

 glass. These figures illustrate : (1) Longitudinal spherical aberration 

 and (2) the focal length of a plano-convex lens and the point from 

 which it is measured. 



(1) In regard to the former it will be seen that the longitudinal 

 spherical aberration is greatest in fig. 17, where the parallel ray* 

 of light fall upon the plane surface, and least where, as in fig. 18, 

 they fall upon the spherical surface. For spherical aberration is the 



FIG. 17. Spherical aberration. 



distance of the focus for any ray passimj throni/h n ///.$ from the 

 jn-i/ici/ial focus of that lens. 



Thus in figs. 17. 18, the spherical aberration is F F' for the ray> 

 R 2 R 2 , and F F" for the rays R 1 R 1 , and the difference between the 



Fig. 18. Spherical aberration. 



spherical aberration of the rays R 1 R 1 and that of the rays R 2 R 2 is 

 F F" - - F F. which is F' F". 



Thus F F' and F F" in (fig. 1 7), cf= - f/ ! ; F F' and F F" 

 in (fig. 18) c/= 7 i where cf signifies the distances F F', 



/ 



F F" respectively, // the distance from the axis where the incident 

 ray enters the lens, and/" the focus. 



(2) In regard to the focal length of a plano-convex lens, it may 

 be incidentally noted that the focal length in fig. 1 7 is twice the radius, 

 measured from the vertex A, that is, A F. But in fig. 18 it is t \vice 

 the radius measured from the point A ; that is, the point Fis distant 

 fr< mi the lens twice the radius less two-thirds the thickness of the lens. 



It will be seen, then, that the amount of spherical aberration is 

 due to the shape of the lens, and is least in a biconvex lens. when the 

 radii of curvature are in the proportion of 6 : 1. n-hi-n the more curved 

 * i/i-face faces the incident light. But when the lens is turned round, 

 so that the other side faces the incident light, the spherical aberration 

 reaches a maximum. 



It would be well for the student who desires to became familiar 

 with these facts, without attempting any profound mathematical 



