Abstract We analyze the behavior of an optical focusing system, used by Richard Feynman in his famous physics classes. The system is a biconvex optical lens with symmetry of revolution around an axis, defined by the property that the rays that start from a point source, located in a focus on the axis, converge to an image point on the other side of the lens, so that the light waves on them arrive simultaneously at this last point. This ensures that the waves of a given frequency, traveling according to different paths from one focus to the other through air and glass, complete the same number of cycles when they reach the image point and therefore interfere in phase with each other. In this work we explicitly show that the profile of the Feynman lens must be hyperbolic, a form that for paraxial rays eliminates the spherical aberration (but not the chromatic aberration) of the lens.