Question

Define wavefront and secondary wavelets. Verify the law of reflection on the basis of Huygens’ wave theory.

Hint:

Huygens' principle: Each point on a wavefront is a secondary source of wavelets. The law of reflection: \(\theta_i = \theta_r\).

Answer 1

Wavefront:
A wavefront is the surface over which an oscillation or wave has a constant phase. It represents all points in space where the wave has the same phase of oscillation at a given instant of time. Wavefronts are perpendicular to the direction of propagation of the wave. For example, in the case of light, spherical wavefronts are generated from a point source.
Secondary Wavelets:
Secondary wavelets are the waves that are produced at every point of a wavefront. According to Huygens' principle, each point on a wavefront acts as a secondary source of spherical wavelets that propagate out in the forward direction. The envelope of these wavelets forms the new wavefront at any later time.
Verification of the Law of Reflection Using Huygens' Wave Theory:
According to Huygens' principle, every point on a wavefront can be considered as the source of secondary wavelets. When a plane wavefront strikes a reflective surface, each point on the surface of the wavefront emits secondary wavelets. The new wavefront is formed by the envelope of these secondary wavelets.
In the case of reflection, consider a plane wavefront approaching a smooth reflective surface. The incident wavefront is at an angle to the surface. The secondary wavelets emanating from each point on the incident wavefront will form a new wavefront, which is reflected at an equal angle on the opposite side of the normal, following the rule that the angle of incidence is equal to the angle of reflection. Thus, Huygens' wave theory verifies the law of reflection: \[ \theta_i = \theta_r \] Where: - \(\theta_i\) is the angle of incidence, - \(\theta_r\) is the angle of reflection.