Abstract: The problem of imaging discussed in the course of optics customarily is under the conditions of “paraxial approximation”. In order to enhance the effectiveness of teaching and their confidence of the theory in practice，we need to give some discussion on non-paraxial approximation of the general situation. It makes clear that directly inverse solution for the change regulation of the refractive index from Fermat’s principle is not a feasible solution. The approximate method will let the refractive index’s functional problem change as the slope of one-dimensional function problem. By using the Euler equation and numerical calculation，we obtain a set of reference parameters for material made.

Key words: variable refractive index, near axis condition, Fermat principle, variational method