Thin dielectric lens reflector

The ray trace equations for a dielectric lens reflector with a tilted linear front surface are derived, and the reflecting profile obtained. A thin lens results when the angle of tilt is such that the lens reflector has zero thickness at the apex. It is found that, for fixed radius and maximum subtended angle at the focus, the reflecting profile is approximately constant with angle of tilt and can, to the same approximation, be constructed from circular arcs.