In accordance with one embodiment, a light mixing and homogenizing apparatus includes a first tubular member and a second tubular member. The first tubular member has a reflective interior surface, a polygonal cross section with a first maximum diameter, and a first number of sides. The first tubular member has a first end and a second end with the first end configured to receive a plurality of incoming light beams. The second tubular member has a reflective interior surface, a polygonal cross section with a second maximum diameter smaller than the first maximum diameter, and a second number of sides that is different from the first number of sides. The second tubular member has a first end disposed adjacent to a first tubular member second end. The second tubular member second end is configured to output a homogeneous light beam comprising a mixture of the plurality of incoming light beams.