Question

State Huygens' principle. Plane wave incident at angle i on reflecting surface. Construct reflected wavefront and prove i=r.

Hint:

Huygens' Principle, Coherence, and Young's Double Slit Experiment

Answer 1

Huygens' Principle and Proof of Law of Reflection

Huygens' Principle

Every point on a wavefront acts as a source of secondary wavelets that spread out in all directions with the speed of the wave. The new wavefront is the surface tangent to these secondary wavelets.

Proof of Law of Reflection

Consider a plane wavefront incident at an angle \(i\) on a reflecting surface. Let \(AB\) be the incident wavefront, \(BC\) the reflected wavefront, and \(OA\) and \(OB\) the corresponding normals.

From Huygens' principle:

Distance covered by the wave in time \(t\) is \(BC = vt\).

Since the wavefronts are symmetric about the normal:

\[ i = r \]