[UPSC IFoS 2014] Geometrical Optics (Q147, 8M)

Write down the mathematical representation of Fermat's principle and explain all the notations used. With the help of a neat diagram, show that this principle can be used to obtain the law of refraction : n_1 \sin \theta_1 = n_2 \sin \theta_2 , where n_1 and n_2 are the refractive indices of the two media while \theta_1 and \theta_2 are the angles of incidence and refraction of the light beam.