Plate-type luminaire comprising a prism plate with a smooth upper plate surface and a prism lower surface formed by a plurality of longitudinal ribs; a cover plate made of translucent material resting on the prism surface; and an optical-waveguide plate on the smooth plate surfaces of the prism plate. The plates are curved continuously in the same direction of curvature, transversely to the longitudinal direction of the longitudinal ribs of the prism plate, at least over most of the plate width, with the longitudinal ribs being located on the inside of the arc of curvature of the prism plate. A reflector plate may be disposed over the waveguide plate, with a smooth or a longitudinally ribbed surface.