  We consider the reflection of light, from a stationary source, off of a
uniformly moving flat mirror, and derive the relativistic reflection law using
well-known properties of conic sections. The effective surface of reflection
(ESR) is defined as the loci of intersection of all beams, emanating from the
source at a given time, with the moving mirror. Fermat principle of least time
is then applied to ESR and it is shown that, assuming the independence of speed
of light, the result is identical with the relativistic reflection law. For a
uniformly moving mirror ESR is a conic and the reflection law becomes a case of
bi-angular equation of the conic, with the incident and reflected beams
coinciding with the focal rays of the conic. A short calculus-based proof for
accelerating mirrors is also given.
