A study was made of the process of internal reflection of a polarized electromagnetic wave from an ellipsoid of revolution. The source of the radiation was at one focus and the reflected signal was assumed to strike a target at the second focus. The objective was to select an arrangement that would provide radiation arriving at the test object with electric vectors that are all parallel to each other. This might, perhaps, be achieved by having reflecting plates only on appropriately chosen parts of the ellipsoid. It was found that the only suitable procedure is to permit rays to be reflected just from a band around the equator of the ellipsoid, which in turn is essentially equivalent to having an elliptical cylinder as the reflector instead of an ellipsoid. As a related matter, radiation energy density was investigated. It was found that the intensity of the radiation arriving at the second focus varies greatly with direction even when the source radiates uniformly.