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

Consider a plane wave AB incident at an angle i on a refracting surface MN. Let .v. be the speed of the wave in the medium and .t. be the time taken by the wavefront to reach from the point B to C. Then BC= v t.
To construct the reflected wavefront, draw a sphere of radius v t from the point A. Let CE represents tangent plane drawn from the point .C. to this sphere. Then AE= BC= v t. In triangles EAC and BAC
`angleAEC= angleABC ("Each is " 90^(@))`
AC = AC (common)
AE= BC (Each equal to vt)
`therefore Delta EAC ~= Delta BAC`
Hence `angleBAC = angleACE`
i=r