Abstract: The ray tracing of the second and higher order reflection is an important and difficult problem. The tracing equations in earlier papers involve several parameters, which leads to taking more time to solve the equations using the numerical searching method. In this paper, the analytical formulations for every reflection point's Z coordinate are deduced by using Fermat's principle and law of reflection in the system of cylinder and cone. Some application examples are given to illustrate that the tracing-time is dramatically reduced and the operational precision is improved. The method presented in this paper can be expanded to solve the ray tracing of the second order reflection of some other model and used as a reference to solve the higher order reflection problem.

Key words: Fermat's principle, the system of cylinder and cone, second-order reflection