A reflector and a light fixture that includes the reflector are provided, where the reflector has a reflecting surface having a shape which closely approximates a determined surface which is series of ellipsoidal section segments, wherein each ellipsoidal section segment has a first focus A and a second focus B, wherein first focus A is the same point for each ellipsoidal section segment, and wherein, for successive ellipsoidal section segments, focus B is at a successive location along a line. In some embodiments, the light fixture additionally comprises a light source, typically located at focus A. The present disclosure enables the projection of a visually striking, linearly extended pattern of light on a wall from a fixture mounted on that same wall, where the fixture may furthermore have very little depth, i.e., orthogonal extension outward from that wall.