How is a wavefront defined? Using Huygen's construction draw a figure showing the propagation of a plane wave reflecting at the interface of the two media. Show that the angle of incidence is equal to the angle of reflection. 

A wavefront is an imaginary surface over which an optical wave has a constant phase. The shape of a wavefront is usually determined by the geometry of the source. 

Huygen's principle:

(i) Every point on a given wavefront acts as a fresh source of secondary wavelets which travel in all directions with the speed of light.
(ii) The forward envelope of these secondary wavelets gives the new wavefront at any instant. 

Laws of reflection by Huygen's principle: 
Let, PQ be reflecting surface and a plane wavefront AB is moving through the medium (air) towards the surface PQ to meet at the point B.
 

Let, c be the velocity of light and t be the time taken by the wave to reach A' from A. 
Then,  AA' = ct.

Using Huygen's principle, secondary wavelets starts from B and cover a distance ct in time t and reaches B'.

To obtain new wavefront, draw a circle with point B as centre and ct (AA' = BB') as radius. Draw a tangent A'B' from the point A'. 

Then, A'B' represents the reflected wavelets travelling at right angle. Therefore, incident wavefront AB, reflected wavefront A'B' and normal lies in the same plane.

Consider ∆ABA' and B'BA'
AA' = BB' = ct       [∵ AA' = BB' = BD = radii of same circle]
BA' = BA'              [common]
∠BAA' = ∆BB'A'     [each 90°]
∴ ∆ABA' ≅ ∠DBA'    [by R.H.S]
∠ABA' = ∠B'A'B    [corresponding parts of congruent triangles] 

∴ incident angle i = reflected angle r
i.e.,                 ∠i = ∠r