SPHERICAL ABERRATIONS. 25 
Hon. In Fig. 15,0, the spherical aberration of a simple collective lens is 
pictured ; here the marginal rays, as in Fig. 14, intercept the axis at B before 
the central rays; in Fig. 15,^, the spherical aberration of a simple negative 
element is given. If the spherical aberration in the lens Fig. 15, a, is equal and 
opposite to that in Fig. 15, b, it is evident that on combining the two lenses 
(Fig. is.c) compensation will result and the resultant spherical aberration 
of the combination for the central and marginal rays will be nil. In Fig. 15, c, 
glasses of different refractive index (positive element crown and negative 
FIG. 15. 
element of higher refracting flint glass) have been chosen to compensate for 
the spherical aberration. It is possible, however, by a proper selection of 
the shapes of the component lenses, to correct for spherical aberration even 
with elements of the same refractive index as indicated in exaggerated form 
in Fig. 1 6. 
If the compensation be not fully attained and the marginal ray still 
intercepts the axis at the point 2 nearer the lens than the central ray P' as 
in Fig. 1 7, a, the lens is said to be spherically under cor reeled; and overcorrected 
if the marginal rays intercept the axis at a point 2 beyond P' as in Fig. 1 7, b. 
FIG. 16. 
It is thus possible, by combining a positive and a negative element of 
proper shapes and refractive indices, to produce a lens free from spherical 
aberration (axial and marginal rays coincide in the image point) . This does 
not signify, however, that the rays from points or zones intermediate be- 
tween margin and axis are automatically corrected. These may be under- 
corrected or overcorrected (Fig. 1 7, c, d) . This residual spherical aberration 
