Fermat's principle in imaging in complex stratified media

We using a problem in mechanics, such as fastest sending messenger to introduce the concept of equivalent distance. We analyzed the choice of a path in kinematics problem. Combining the application of Fermat's principle in the law of refraction, we established the corresponding analogy relationships of optical and kinematics physical description. The analogy method presented in this paper would be helpful for deep understanding of optical concepts such as: optical path etc. And provide a deeply understanding reference method for Fermat's theorem. especially in a complex stratified media.