A directional lamp comprises a light source, a beam forming optical system configured to form light from the light source into a light beam, and a light mixing diffuser arranged to diffuse the light beam. The light source, beam forming optical system, and light mixing diffuser are secured together as a unitary lamp. The beam forming optical system includes: a collecting reflector having an entrance aperture receiving light from the light source and an exit aperture that is larger than the entrance aperture, and a lens disposed at the exit aperture of the collecting reflector, the light source being positioned along an optical axis of the beam forming optical system at a distance from the lens that is within plus or minus ten percent of a focal length of the lens.