A solar furnace consisting of a paraboloid of revolution which tracks the sun and reflects radiation to a hyperboloid of revolution having a common focus with the paraboloid is analyzed to determine the concentration available, using various eccentricities. The hyperboloid, in turn, reflects radiation to a focal plane placed at various distances from the vertex of the paraboloid. The ideal concentration is determined using the largest radius of all the rays from the sun falling on the paraboloid, this radius being the dis-tance from the pierce point of the ray, in the focal plane, to the hyperboloid focal point. The concentrations can be augmented using a compound paraboloidal concentrator, and the ideal augmented concentration is developed for various combinations of eccentricity and vertex distances. The effect of scattering angles for the paraboloid and hyperboloid on the ideal concentration is shown separately and jointly.