along the axis in a Series of focal points as in Fig. 39. This is 

 chromatic aberration. This aberration is of opposite sign in 

 positive and negative lenses so that the combination of a positive and 

 a negative lens of the same power and same kind of glass will be 

 free from chromatic aberration but it will have no power. Fortu- 

 nately, glasses of widely different dispersive powers are available so 

 that we can make a negative lens of relatively low power which has 

 chromatic aberration sufficient to neutralize that of a relatively 

 strong positive lens. The combination will then be achromatic 

 but w ill have a residual positive power equal to the algebraic sum 

 of the powers of the elements. 



ai 



Fig. 40 



Light incident on the marginal zones of a lens is refracted 

 relatively more strongly than rays incident near the axis, so that, 

 even if we restrict ourselves to light of a single color, the incident 

 beam is brought, not to a single focal point, but to a series of focal 

 points as shown in Fig. 40. The magnitude of this so called 

 spherical aberration varies with the shape of the lens and is a min- 

 imum (not zero) when the work of refraction is equally divided be- 

 tween the two surfaces. The spherical aberration of a negative lens 

 is of such a sign as to tend to neutralize that of a positive lens. 

 Hence, after the focal lengths and glasses have been selected in such 

 a manner as to eliminate the chromatic aberration, the positive and 

 negative elements of the achromatic lens may be so shaped that their 

 spherical aberrations are equal in amount and therefore neutralize. 

 The combination is then free from primary chromatic and spherical 

 aberrations. 



It must not be assumed, however, that a so-called achromatic 

 lens will produce an absolutely colorless image. The ratio of the 

 dispersions of the crown and flint glasses available for telescope 

 objectives are not equal for all parts of the spectrum so it is possible 

 to bring to a common focus only two colors. This leaves some un- 

 corrected chromatic aberration known as secondary spectrum. 

 Further, chromatic correction can be effected for but one zone of the 

 objective. Corrected for the axial zone an objective will show over 

 correction at the margin, a defect which becomes rapidly more 

 serious as the relative aperture is increased. Up to a certain point, 

 however, we believe the increase in brightness gained by increase in 

 aperture more than counterbalances the increase of color in the 

 image. 



81 



