SPHERICAL ABERRATION. 



63 



producing cones of light intersect, C C the infinitely-thin field- 

 lens, a I the (unformed) objective-image, and a' b' the real image 

 of the field-lens. If the field-lens were aplanatic, the cones of 

 light directed towards a and b (represented in the figure by 

 simple lines) would cut the optic axis in the same point in 

 which the more central cones, for instance, JE* m and E* n, 

 intersect. Any points m, n . . . . in the plane a b would there- 

 fore have corresponding positions in the real image a b', for the 

 proportions are 



am : me = a/j, : ///y = am' : me, 

 and, similarly, 



bn : nc = ftv : vy b'n : n'b'. 



The objective-image would therefore undergo an entirely uniform 

 diminution. 



This uniformity is, however, destroyed through the stronger 

 refraction of the peripheral pencils. While the pencils directed 



FIG. 22. 



FIG. 23. 



FIG. 24. 



to the points m and n are refracted to o, those proceeding to a 

 and b intersect in o'. In consequence of this, the points a and 

 m' on the one side, and &' and ri on the other, as shown by 

 the figure, are brought nearer to each other than would be 

 the case if the diminution were uniform. The same reasoning 

 applies, of course, to any other points which lie near to each 

 other in a radial direction. We therefore arrive at the general 

 conclusion, that the surface-elements of the objective-image are 

 the more diminished, in consequence of the spherical aberration 

 of the field-lens, the greater their distance from the optic axis. 

 Accordingly, the objective-image of a net-work of squares, for 

 instance, Fig. 22, would appear in the real image of the field- 

 lens as in Fig. 23. 



The effect is exactly the opposite if, under the same conditions, 



