Q.State Huygens' principle. Establish the laws of reflection of light using Huygens' principle.

Huygens' principle constructs a new wavefront as the envelope of secondary wavelets from the old one; applying this construction to a wave reflecting off a plane surface, and matching up triangle geometry, directly yields angle of incidence = angle of reflection.

Huygens' Principle states:

1. Every point on a given wavefront (an existing wavefront) acts as a fresh source of secondary spherical wavelets, which spread out with the same speed as the original wave.
2. The new (later) wavefront at any subsequent instant is given by the surface that is tangent to all these secondary wavelets - i.e. their common envelope, drawn on the forward side.

Deriving the law of reflection using Huygens' construction:

Let a plane wavefront AB be incident on a plane reflecting surface MN at angle i (angle of incidence, measured from the normal). Let v be the speed of the wave, and let the wavefront take time t to travel from the point B (which is still in the incident medium) to reach point C on the mirror.

While this happens, the point A of the wavefront (which reaches the mirror first) becomes a source of a secondary wavelet, and this wavelet spreads out into the same medium as a hemisphere of radius vt (since A has had the full time t to radiate while B was still travelling to C):

AD = vt = BC (since BC is the distance B travels to reach the mirror at C, in time t, at the same speed v)

So the two right triangles ABC and ADC (right angles at B and D respectively, since AB and CD are wavefronts perpendicular to their respective rays) share the same hypotenuse AC, and have equal sides BC = AD. Therefore, by the RHS (right angle-hypotenuse-side) congruence criterion:

triangle ABC is congruent to triangle ADC

This congruence gives angle BAC = angle DCA (call this angle r).

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