90° rotation of a line source by reflection

A new reflecting surface that re-orients a line-source through an angle of
90\deg
is discussed. Several curves on the surface are simple parabolas and ellipses, but the expression for an arbitrary curve on the surface is a fourth-order equation. The curves are derived by preserving phase relationship between the line source and the rotated line using geometrical optics. The intensity distribution on the rotated line is found by numerical integration.