Q.What is the meaning of wavefront? Explain the laws of reflection on the basis of Huygens' principle of wavefront. OR Determine the following for the given A.C. circuit:

A wavefront is a surface of constant phase; Huygens' secondary-wavelet construction on a plane wavefront reproduces the law of reflection $i=r$ with incident ray, reflected ray and normal coplanar.

(This is the main alternative of an internal-choice (OR) question.)

Meaning of wavefront. A wavefront is the continuous locus of all the points of a medium which are vibrating in the same phase at a given instant. A point source gives spherical wavefronts; a very distant source gives plane wavefronts. The direction of propagation (a 'ray') is always perpendicular to the wavefront.

Huygens' principle. Every point on a wavefront acts as a source of secondary spherical wavelets which spread out in the forward direction at the wave speed; the new wavefront at a later instant is the forward envelope (tangent surface) of these secondary wavelets.

Laws of reflection by Huygens' principle. Let a plane wavefront $AB$ strike a reflecting surface $MN$. Let $A$ touch the surface first while $B$ still has to travel to the surface, reaching point $C$ after time $t$; in that same time the secondary wavelet from $A$ spreads a distance $AE = BC = c\,t$.

• Draw the reflected wavefront $CE$ (tangent from $C$ to the wavelet of radius $AE$ centred at $A$).
• In right triangles $ABC$ and $AEC$: $BC = AE\;(=ct)$, hypotenuse $AC$ common, and $\angle ABC = \angle AEC = 90^\circ$. Hence the triangles are congruent, giving $\angle BAC = \angle ECA.$ These equal angles are exactly the angle of incidence $i$ and the angle of reflection $r$ (measured from the normal). Therefore $\boxed{i = r}$ and the incident ray, the reflected ray and the normal all lie in the same plane — the two laws of reflection. …