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127. In order to examine this additional confusion we will suppose a beam of Sun-light to fall on a lens, formed so as to collect each kind of homogeneous light accurately to one point without aberration.

Let then QR (Fig. 139.) represent a pencil of compound light incident at R. This will be divided by the refraction into several pencils Rv, Ri, Rb, , if v, i, b, g, y, o, r, be the points to which the violet, indigo, blue, green, yellow, orange, and red rays converge.[1] And if rays are admitted to all points on the surface of the lens, the points v, i, &c. will be the vertices of so many cones of light of the different colours.

As all the rays do not converge to one point, it is important to know at least where they approach most nearly to it, or where they are all collected in the least space, and how great that space is, which is, in technical language, to require the center and diameter of the least circle of chromatic aberration or dispersion.

A little consideration will easily make it clear that if Bv, bv, Br, br, (Fig. 140.) be the extreme violet and red rays from opposite points of the lens, all the refracted light from the section BAb of the lens will be found in the spaces between the lines Bv, Br, bv, br, all produced without limit, and that the smallest space occupied by them all is the line nmo which joins the intersections of Br, bv; Bv, br respectively: no is therefore the diameter and m the center of the required circle of aberration.

Now mn=AB·mr/Ar; and again, mn=ABmv/Av; so that if we add these together, we shall have

no=Bbvr/Ar+Av=BbArAv/Ar+Av,

Am=Av+vm=Av+Av·nm/AB=Av(1+no/Bb)=2Ar·Av/Ar+Av.


  1. We suppose here that there are seven distinct parcels of colours, each refracted to its proper focus, but as in the most perfect experiment of the prismatic spectrum there are no intervals between the colours, the number of foci should probably be infinite.