A radiation gathering reflector and a method of making a radiation gathering reflector. Resin impregnated fibrous material is wound onto a mandrel which has a pair of opposing surfaces of revolution each of which has a shape corresponding to a predetermined shape of the inner reflector surface, and the resin is allowed to polymerize to form a composite which includes two integrally connected structural support members. An equatorial cut is formed in the composite to separate the support members from each other and from the mandrel. Then, a reflective surface is formed on the inner surface of at least one of the separated support members for gathering radiation. Alternatively, the reflective surface is formed on the surface of the mandrel and the resin impregnated fibrous material is wound onto the reflective surface and allowed to polymerize to form the composite. The forming of the radiation gathering reflector by a polar winding process such that a greater mass of material is located at the center portion is preferred to provide increased structural support at the center portion for attachment of radiation absorbing components so that the support member may have a thin edge portion and therefore require less material, be inexpensive, and be of lighter weight. Such a radiation gathering reflector also preferably includes a plurality of strengthening ribs which extend between the center portion and the edge portion and which cross each other in diamond-shaped configurations to provide increased strength and stiffness to the reflector support member.