Question

State Huygen’s principle and verify laws of reflection using suitable diagram.

Answer 1

Laws of reflection on the basis of Huygens' wave theory:

Consider a plane wavefront AB that is perpendicular to the plane of paper and is incident on the plane reflecting surface XY, as represented in Fig.

The wavefront first strikes the reflecting surface at B, then at successive places towards C. Huygens' principle states that secondary wavelets grow at c from each point on BC. As the disturbance from A reaches C, the secondary wavelets from D must spread over a hemisphere of radius BD = AC = C, where t is the travel time from A to C. 

Let angles of incidence and reflection be i and r, respectively. In ΔABC and ΔDCB, we have

∠BAC = ∠CDB

BC = BC

AC = BD

ΔABC ≅ ΔDCB

Hence, ∠ABC = ∠DCB

or ∠i = ∠r

The angle of incidence equals the angle of reflection. This confirms the first law of reflection. The incident ray SB, normal BN, and reflected ray BO are perpendicular to the incident wavefront AB, reflecting surface XY, and reflected wavefront CD, all of which are perpendicular to the plane of the paper. As a result, they all lie on the same plane. This proves the second law of reflection.