In the fig. is shown a wave front AB on a reflection surface. According to Huygens’s wave theory every point on the wave front is a source of secondary wavelets which travel in all directions with the velocity of light in the medium. The forward, locus of the secondary wavelets gives us the position of the reflected wave front. In the fig, the wavelets from B strike XY at A’ such that BA’ = c × t. With A as center and radius ct, draw an arc AB’ = ct. From A, draw a tangent to this arc to meet it at B’. Then A’B’ is the reflected wave front. Produce the ray forwards to meet XY at P. From P, draw PD’ and PN ⊥ B’A’ and BA’ respectively. Then A’B’ will be a true reflected wave front of
Now, Δs AA'B and AA'B' are congruent.
∴ A'B is the times reflected wavefront
Again, ∠BAA' = B'A'A = ∠i = ∠r
