Solution
(a) Law of Reflection: Assume that XY is a reflecting surface onto which an oblique wavefront is incident. Let v be the wavefront's speed, and the wavefront meets the surface XY at A at time t = 0. After t seconds, the wavefront's point B reaches the surface's point B'. Each point of the wavefront, according to Huygen's principle, works as a source of secondary waves. When the wavefront's point A collides with the reflecting surface, it is unable to travel any further due to the existence of the reflecting surface; however, the secondary wavelet originating from point A begins to spread in all directions in the first medium at v. As the wavefront AB moves forward, its points A1, A2, A3 K, and so on, collide.
First, in time t, the secondary wavelet begins from point A and crosses the distance AA' (=vt) in the first medium. The point B of the wavefront, after travelling a distance BB', reaches point B' (of the surface) at the same time t, from which the secondary wavelet now begins. We now draw a spherical arc of radius AA' (= vt) with A as the centre and tangent A' B' on this arc from point B'. As the incidence wavefront AB moves forward, secondary wavelets emerge from places between A and B one by one, touching A' B' at the same time. Wavefront A' B' represents the new position of AB according to Huygen's principle, i.e., A' B' is the reflected wavefront corresponding to incident wavefront AB.
Now in right-angled triangles ABB' and AA' B' ∠ABB' = ∠ AA' B' (both are equal to 90°) side BB' = side AA' (both are equal to vt) and side AB' is common i.e., both triangles are congruent.
∴ ∠BAB' = ∠AB' A
i.e., incident wavefront AB and reflected wavefront A' B' make equal angles with the reflecting surface XY. As the rays are always normal to the wavefront, therefore the incident and the reflected rays make equal angles with the normal drawn on the surface XY, i.e., angle of incidence i = angle of reflection r
The second law of reflection is this. Because AB, A' B', and XY are all in the same plane as the paper, the perpendiculars that are dumped on them will be in the same plane as well. As a result, the incident ray, reflected ray, and normal at the point of incidence are all in the same plane. This is the first reflection law. Huygen's idea thus explains both reflection laws.
