Geometrical considerations on the directivity of reflected light from a paraboloidal mirror

A divergence angle of the light emanated from an optical source composed of a source of light with finite size and a paraboloidal reflector is analyzed on the basis of geometrical considerations. The divergence angle distributions of the reflected light rays from each reflection point on the paraboloidal mirror are numerically calculated as parameters of the shapes of a lamp arc body and a paraboloidal reflector. It has been found from the analyses that the divergence angle can be reduced by prolongation of the optical path length PO to the reflection point P on the paraboloidal mirror from the focal point O of it, at which the center of the extent of the arc is located. A new approach different from conventional one to reduce the divergence angle of the light rays emanated from the optical source is proposed. The new configurations of the optical source composed of a source of light with finite size and a paraboloidal reflector or a spheroidal converging reflector are shown and discussed.