Using Fermat's principle to prove the law of reflection

[etothey]

Homework Statement

Fermat’s principle states that the path of a light ray between two points is such that the time to traverse that path is an extremum (either a minimum or a maximum) when compared with the times for nearby paths. Consider two points A and B on the same side of a reflecting surface, and show that a light ray traveling from A to B via a point on the reflecting surface will take the least time if its path obeys the law of reflection. Thus, the law of reflection follows from Fermat’s principle.

Homework Equations

Triangle symmetry

The Attempt at a Solution

would this be a reasonable proof without involving to much maths? http://www.math.uiowa.edu/~stroyan/CTLC3rdEd/ProjectsOldCD/estroyan/cd/27/index.htm

 

[supratim1]

looks a good enough way to prove it.