The three-lense problem

With how many lenses can we build "all" optical systems? In the paraxial re gime (rays of small angles and thin lenses), the problem is reduced to one solvable with matrices and some wit. It has been concluded in the standard reference [E.C.G. Sudarshan, N. Mukunda and R. Simon, Optica Acta 32 (1985) 855] that the minimum is three lenses. Our analysis is simple and reveals better the structure of the boundaries between different optical configurat ions. We note that to form equivalent images only two lenses are required. We say what to do when we only have at hand lenses of a few focal distances .