Abstract: A reflector for coupling light from a light source into an optical waveguide includes input and output ends, a central axis and a reflecting surface disposed around the central axis. A light source, such as an arc lamp, is positioned on the central axis at the input end of the reflector. An input end of an optical waveguide is positioned on the central axis at the output end of the reflector. The reflecting surface has a first section adjacent to the input end with a first curvature that is concave toward the central axis, a second section adjacent to the output end with a second curvature that is concave away from the central axis, and an inflection section between the first and second sections. The first and second curvatures are selected to reflect light through the output end of the reflector within a prescribed range of angles that corresponds to the acceptance angle of the optical waveguide.