  The space ${\Bbb{L}}$ of oriented lines, or rays, in ${\Bbb{R}}^3$ is a
4-dimensional space with an abundance of natural geometric structure. In
particular, it boasts a neutral K\"ahler metric which is closely related to the
Euclidean metric on ${\Bbb{R}}^3$. In this paper we explore the relationship
between the focal set of a line congruence (or 2-parameter family of oriented
lines in ${\Bbb{R}}^3$) and the geometry induced on the associated surface in
${\Bbb{L}}$. The physical context of such sets is geometric optics in a
homogeneous isotropic medium, and so, to illustrate the method, we compute the
focal set of the $k^{th}$ reflection of a point source off the inside of a
cylinder. The focal sets, which we explicitly parameterize, exhibit unexpected
symmetries, and are found to fit well with observable phenomena.
