A unique focusing property of a parabolic mirror for neutrons in the   gravitational field: geometric proof
  An extraordinary focusing property of a parabolic mirror for ultracold neutrons in the presence of the gravitational field was first reported by A. Steyerl and co-authors. It was shown that all neutrons emitted from the focus of the mirror will be reflected back upon the same focus point passing, in between, a point of return in the gravitational field. The present note offers a complementary geometric proof of this feature and discusses some implications. 
S. Masalovich
physics.class-ph