ACHROMATISM. 177 



convex, if the curve and thickness of the two lenses 

 be properly adapted, the marginal portions of the con- 

 cave correct the too great convergence of the mar- 

 ginal rays produced by the convex lens, and so the 

 rays are brought to nearly the same focus. An idea 

 of this action may be obtained from fig. 25, the dotted 

 lines indicating the direction which the rays would 

 take, if passing through the convex lens only. 



A lens in which the spherical aberration is cor- 

 rected is said to be aplanatic. 



Achromatism. Supposing the spherical aberration 

 of a lens to be corrected, there still remains the 

 chromatic aberration (p. 173) ; for although the cen- 

 tral or mean coloured rays may meet at a focus, the 

 other coloured rays belonging to the same compound 

 or ordinary ray will meet at different foci, so that a 

 series of coloured images of the object will be formed 

 at different distances from the lens ; hence, at which- 

 ever focus the object is viewed, it will appear coloured. 



Now the coloured primary rays can only be made 

 to coincide in direction, so that the light parts of an 

 object may appear white, by refraction. And the 

 correction is produced by the same plano-concave 

 lens as that which corrects the spherical aberration. 

 But in this case the relative dispersive powers of the 

 media composing the convex and the concave lenses 

 form the point to be considered. If the dispersive 

 power of the media of which the convex and concave 

 lenses are composed were the same, the dispersive 

 power of the convex lens would be in excess, and the 

 coloured rays in each compound ray could not become 

 parallel. But by forming the concave lens of a more 

 highly dispersive medium, with a less proportional 

 mean refraction than the convex, when the curves of 

 the surfaces and the relative thickness of the lenses 

 are properly adjusted, the dispersive action of the 

 concave lens may be made equal to that of the con- 

 vex ; and being exerted in the opposite direction, the 



