Fermat's  Principle    It  states  that "the path taken by light between  two points is such that the time of passage is minimum". The  Fermat's principle is fundamental in deciding the path taken by  a  ray of light. The rectilinear propagation of light, laws of reflection and refraction, all follow as consequence of this law.

We  will  illustrate the law in case of reflection. Consider a point  A, from where  a  ray  of light travels to point B after suffering reflection in the plane mirror mm' (see  fig.  f2).  We  wish to find the path applying the Fermat's principle. Let's drop perpendiculars from A and B which meet mm' at O and O' respectively. Let OO'= p, and AQB the path of light. The path length L is

L = d + d' = (h2+ x2)1/2+ [h'2 + (p-x)2]1/2

Taking  differential  of  L  with respect to x and setting it to zero, we obtain,

x/d = (p-x) / d'

or sin q = sin q '

giving q = q '.

That  is  angle  of reflection equal to angle of incidence. In an exactly similar fashion we can  prove  the  Snell's  law  of refraction.