A generalization of Prentice's law for lenses with arbitrary refracting surfaces

A generalization of the Prentice's law is presented in this paper. The idea consists of removing some (but not all) of the approximations that comprise the paraxial approach. In that way, we obtain a new formulation that permits us to compute the prismatic power of a lens made up of arbitrary refracting surfaces, and to improve the precision obtained by Prentice's law when applied to monofocal lenses. The resulting formalism is simple and manageable and its derivation leads us to a precise definition of the local dioptric power matrix, introduced in a previous paper, as well as a better understanding of the same.