Question

Using Huygen’s wave theory of light, show that the angle of incidence is equal to angle of reflection in case of reflection of a plane wave by a plane surface. 

Answer 1

Consider a plane wave AB incident at an angle i on a reflecting surface MN. If v represents the speed of the wave in the medium and if τ represents the time taken by the wavefront to advance from the point B to C then the distance BC = vτ, In order to construct the reflected wavefront, a sphere of radius = vτ, is drawn from the point A as shown in the adjacent figure. Let CE represent the tangent plane drawn from the point C to this sphere. 

∴ AE = BC = vτ , ∠ABC= ∠CEA = 90°, AC is common. 

Triangles EAC and BAC are congruent. 

∴ i = r.