Abstract: The mathematical model and conventional solution of catenary and mirage are briefly introduced at first. Then， the catenary equation is discussed in terms of Snell’s Law， and the forming of a mirage is described on the basis of Lagrangian. Based on the analysis of the relations between these two mathematical models， the value of the connections between Hamilton’s principle and Fermat’s principle is re-emphasized for the physics education at university.

Key words: Hamilton principle, mirage, Fermat s principle