Huygen was the first scientist who proposed the idea of wave theory of light. He said that the light propagates in form of wavefronts. A wavefront is an imaginary surface at every point of which waves are in the same phase. For example the wavefronts for a point source of light is collection of concentric spheres which have centre at the origin. w 1 is a wavefront. w 2 is another wavefront

The radius of the wavefront at time ‘t’ is ‘ct’ in this case where ‘c’ is the speed of light. The direction of propagation of light is perpendicular to the surface of the wavefront. The wavefronts are plane wavefronts in case of a parallel beam of light.

Huygen also said that every point of the wavefront acts as the source of secondary wavelets. The tangent drawn to all secondary wavelets at a time is the new wavefront at that time. The wavelets are to be considered only in the forward direction (i.e. the direction of propagation of light) and not in the reverse direction. If a wavefront w 1 at time t is given, then to draw the wavefront at time t + Δ t take some points on the wavefront w 1 and draw spheres of radius ‘c Δ t’. They are called secondary wavelets.

Draw a surface w 2 which is tangential to all these secondary wavelets. w 2 is the wavefront at time
‘t + Δ t’. Huygen proved the laws of reflection and laws of refraction using concept of wavefronts.

(i) A point source of light is placed at origin, in air. The equation of wave front of the wave at time t, emitted by source at t = 0, is (take refractive index of air as 1)