  We give an optical physicist view of the problem of the trajectories in a
polygonal billiard using only basic facts of Optics and the theory of functions
of a complex variable. This approach allow us to stablish a certain
correspondence between n-gon billiards and one-holed 2n-punctured tori.
Therefore the existence of periodic trajectories in a certain polygon becomes
the problem of the existence of closed geodesics in its associated torus.
