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

Wavefront = surface of constant phase; secondary wavelets = wavelets from each point of it. Huygens' construction on a plane mirror gives ∠i = ∠r.

Wavefront. A wavefront is the locus (continuous surface) of all the points of a medium that are vibrating in the same phase at a given instant. For a point source it is spherical; far from the source it is effectively plane.

Secondary wavelets. According to Huygens' principle, every point on a given (primary) wavefront acts as a fresh source of disturbance, sending out small spherical wavelets called secondary wavelets, which travel with the speed of light in the medium. The forward envelope (tangential surface) of all these secondary wavelets after a time t gives the position of the new (secondary) wavefront.

Proof of the law of reflection (Huygens' theory).

Consider a plane wavefront AB incident on a plane reflecting surface XY, making an angle of incidence i. Rays travel perpendicular to the wavefront. Let the wavefront reach A first; while the disturbance travels from B to the surface at C, a secondary wavelet spreads from A.

• Time for the wave to go from B to C = time for the secondary wavelet from A to reach the new wavefront. If c is the wave speed and the time is t, then $BC = c\,t \quad\text{and}\quad AD = c\,t,$ so BC = AD (equal radii of the two wavelets).
• Draw the reflected wavefront CD tangent to the wavelet of radius AD centred at A.

Now compare the two right triangles ABC and ADC (right angles at B and D respectively):

• AC is common (the hypotenuse of both),
• BC = AD (shown above). …