Question

Fermat's principle states that "light travels between two points along the path that requires the least time, as compared to other nearby paths." From this principle, derive (a) the law of reflection and (b) the law of refraction (Snell's law). [Hint: choose two appropriate points so that a ray between them can undergo reflection or refraction. Draw a rough path for a ray between these points, and write down an expression of the time required for light to travel the arbitrary path chosen. Then take the derivative to find the minimum.]