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Recent work by Jaffe and Scardicchio has expressed the optical approximationto the Casimir effect as a sum over geometric quantities. The first two authorshave developed a technique which uses the complex geometry of the space oforiented affine lines in ${\Bbb{R}}^3$ to describe reflection of rays off asurface. This allows the quantities in the optical approximation to the Casimireffect to be calculated.  To illustrate this we determine explicitly and in closed form the geometricoptics approximation of the Casimir force between two non-parallel plates. Bymaking one of the plates finite we regularise the divergence that is caused bythe intersection of the planes. In the parallel plate limit we prove that ourexpression reduces to Casimir's original result.Comment: 25 pages, 8 figures, AMS-LATE

THE CASIMIR EFFECT BETWEEN NON-PARALLEL PLATES BY GEOMETRIC OPTICS