A luminaire 1 comprising a light-directing element 3, e.g. a reflector, having a light emission window 5. Said reflector has a shape for directing light originating from an electric light source 7 into an optical fiber system 9 positioned in front of the light emission window. The optical fiber system comprises a bundle of optical fibers 11. Said shape is calculated in accordance with a ray-tracing algorithm which takes into account that said light source is voluminous, e.g. a Light Emitting Diode. The reflector has a shape which is composed of n solids of revolution of parabolic sectors 13, wherein said (adjoining) parabolic sectors form an integral surface 15. The invention further relates to a dynamic road marking unit 19.