Question

Using Huygen's wave theory of light, show that the angle of incidence is equal to the angle of reflection. Draw a neat and labelled diagram.

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 T represents the time taken by the wavefront to advance from point B to C, then distance BC = vt.

In order to construct the reflected wavefront, a sphere of radius = vt is drawn from point A, as shown in the figure. Let CE represent the tangent plane drawn from the point C to this surface.

∴ AE = BC = vt

∠ABC = ∠CEA = 90°

Here AC is common.

∴ ΔEAC ≅ ΔBAC

Hence i = r.