Page:Optics.djvu/117

 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. 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