A simple but general treatment of reflection and refraction at spherical surfaces is based on properties of nodal points and the specification of wave fronts by their convergences. Rules for the location and description of images are justified and extended to the images formed by thin lenses, the positions of whose nodal points make apparent an analogy with single refracting surfaces. The formula for the change in convergence of a wave front proceeding in a homogeneous and isotropic medium is applied to describe the images of axial objects, to derive Newton's relation in generalized form, and to consider refraction by separated refracting surfaces of unspecified powers. Solutions to five numerical problems, obtained by methods advocated in the paper, are appended.