Abstract: Fermat’s principle is applied to derive the condition for the interface of reflection and refraction to enable the perfect convergence of parallel beams at a single point. An imaging law of each optical elements with paraxial light is obtained by examining the light propagation through the rotating parabolic surface, ellipsoid surface, spherical surface and the spherical lens. With the ZEMAX software, we simulate the light propagation and obtain optical path diagram for the aforementioned optical elements. Furthermore, we deduce an object image equation for the spherical surface, spherical surface and thick lens under the condition of non-paraxial approximation by applying Fermat’s principle. Namely, a unique image point can be observed only for paraxial objects in paraxial light, and the paraxial approximation is the necessary and sufficient condition for ideal imaging.