Using Huygens principle, show that the angle of incidence is equal to angle of reflection during a plane wave front reflected by a plane surface.

Explanation

MN- reflecting surface
AB= Incident plane wave front
i- angle of incidence
r-angle of reflection
v-speed of light in the medium

If v represents the speed of the wave in the medium and if `tau` represents the time taken by the wave front to advance from the point B to C then the distance BC is,
`BC = v tau` .....(1)
In order to construct the reflected wave front, a sphere of radius `= v tau`, is drawn from the point A as shown in the figure. The tangent plane CE drawn from the point C to this sphere represents reflected wave front.
`therefore AE= BC = v tau, angle ABC= angle CEA= 90^(@), AC` is common.
Triangles EAC and BAC are congruent
`therefore i= r` .....(2)
This is the law of reflection.