  Recent work by Jaffe and Scardicchio has expressed the optical approximation
to the Casimir effect as a sum over geometric quantities. The first two authors
have developed a technique which uses the complex geometry of the space of
oriented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off a
surface. This allows the quantities in the optical approximation to the Casimir
effect to be calculated.
  To illustrate this we determine explicitly and in closed form the geometric
optics approximation of the Casimir force between two non-parallel plates. By
making one of the plates finite we regularise the divergence that is caused by
the intersection of the planes. In the parallel plate limit we prove that our
expression reduces to Casimir's original result.
