The invention provides method and apparatus for making light-weight honeycomb mirrors by assembling fused quartz ribs in a honeycomb pattern so that rib ends are proximate other rib ends to form rib junctions. A laser beam is then directed at the rib junctions to weld the rib ends together to form a honeycomb structure having a plurality of rib-defined cells or modules therein. Fused quartz plates of matching size are then positioned across the so-formed rib cells and welded by directing a high powered laser beam at the edges of the plates and adjacent ribs to weld the plates to the rib cells of the honeycomb structure and define a honeycomb mirror blank. The surface of the plates of, e.g. fused quartz, are then ground and polished to a mirror finish and a reflective coating added, to complete the light-weight honeycomb mirror by the method and apparatus of the invention.