Reflection of Plane Waves using Huygens Principle

When a light wave encounters a reflecting surface, such as a mirror, the incident wavefront strikes the surface. According to Huygens’ principle, each point wavefront behaves as a source of secondary wavelets.

These secondary wavelets spread out spherically from each point. The reflected wavefront is formed by the tangent points of the secondary wavelets. This new wavefront is perpendicular to the reflecting surface at each point.

Thus, Huygens’ principle helps to explain the laws of reflection: the angle of incidence is equal to the angle of reflection, and the incident ray, the normal, and the reflected ray all lie in the same plane.

Laws of Reflection

According to the law of reflection:

• When light hits a surface, the incoming ray, the reflected ray, and the imaginary line perpendicular to the surface (called the normal) all lie in the same plane. This means that the reflected light stays in the same flat sheet as the incoming light and the normal line.
• The angle of incidence is equal the angle of reflection.

Laws of Reflection using Huygens Principle

The laws of reflection using Huygens’ principle is proved below:

Assume that AB is the plane wavefront incident on the plane mirror M₁ M₂ .

Let ∠BAA’ = ∠i be the incident angle. The incident rays to wavefront AB are 1, 2 and 3.

According to Huygens’ Principle, every point along the wavefront AB acts as a source of secondary wavelets.

Let’s assume that the secondary wavelets from point B reach point A’ in time t.

BA’ = c × t ……………………..(1)

where, c = velocity of light in vacuum

Let secondary wavelets from point A goes at point B’ in time interval t .

AB’ = c × t ………………………(2)

If you join A’ and B’, the reflected wavefront will be A’B’.

The reflected rays perpendicular to A’B’ are 1′, 2′ and 3′. Also, let B’A’A is equal to r( the reflection angle ).

We use similar triangles AA’B and AA’B’.

BA’ = AB’ (From (1) and (2))

∠B = ∠B’ (Both are 90)

AA’ = AA’ (Common Base)

Hence, triangles AA’B and AA’B’ are congruent.

∠i = ∠r

Thus law of reflection using Huygens’ law is proved.

Huygens’ principle is a fundamental concept in wave optics that explains the behavior of waves, including both refraction and reflection, based on the principle of wavefront propagation. According to Huygens’ principle, every point on a wavefront serves as a source of secondary spherical wavelets, and the new wavefront at any instant is the envelope of these secondary wavelets.

In this article, we will learn in detail about the Huygens Principle, reflection, and refraction using the Huygens principle.