  Using the ray-optics approximation, we analyze the Casimir force in a two
dimensional domain formed by two metallic blocks adjacent to parallel metallic
sidewalls, which are separated from the blocks by a finite distance h. For h >
0, the ray-optics approach is not exact because diffraction effects are
neglected. Nevertheless, we show that ray optics is able to qualitatively
reproduce a surprising effect recently identified in an exact numerical
calculation: the force between the blocks varies non-monotonically with h. In
this sense, the ray-optics approach captures an essential part of the physics
of multi-body interactions in this system, unlike simpler pairwise-interaction
approximations such as PFA. Furthermore, by comparison to the exact numerical
results, we are able to quantify the impact of diffraction on Casimir forces in
this geometry.
