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Microwaves propagated between two doubly‐curved parallel conducting surfaces, in the geometrical optics approximation, follow rays obeying Fermat's principle. The optical distance in this case is determined both by the index of refraction of the material between the surfaces and by the curvature of the surfaces. The focusing properties of such a parallel plate lens is fully specified by giving the metric of the two‐dimensional optical space associated with the mean surface of the guide. A family of equivalent lenses is shown to exist, and formulas are obtained that permit one to go from any one of these lenses to any other. Furthermore, conditions are given for there to exist in a family of equivalent lenses a lens employing a unit index of refraction everywhere. Of particular interest is the demonstration that the Rinehart analog of the Luneberg lens and the RCA ``R‐2R'' lens are members of a two‐parameter family of lenses with analogous focusing properties.