  The free surface of hydrodynamic waves behaves as a time-varying planar
curvilinear mirror, whose focal properties determine the light intensity
distribution in a reflected light beam. Variational criteria for determination
of foci of planar curvilinear mirrors illuminated by a coplanar light source
are studied in the realm of Geometric Optics. Intrinsic functions of the
optical setup (called focal potentials in the text) which are stationary at
mirror points corresponding to cusp points of the caustic of reflected light
rays are analyzed. The eccentricity of the osculating conic defined at each
mirror point is shown to be a dimensionless, coordinate independent focal
potential. An application to numerical analysis of light focusing by
laser-illuminated hydrodynamic solitons is presented.
  OCIS codes: 080.0080 (Geometric Optics) 110.0110 (Imaging Systems) PACS code:
47.35.Fg (Solitons in Fluids)
