Consider a plane wave front AB incident obliquely on a plane reflecting surface MM’. Let us consider the situation when one end A of wave front strikes the mirror at an angle i but the other end B has still to cover distance BC. Time required for this will be t = BC/ c.
According to Huygens’s principle, point A starts emitting secondary wavelets and in time t, these will cover a distance c,t = BC and spread. Hence, with point A as center and BC as radius, draw a circular arc. Draw tangent CD on this arc from the point C. Obviously. CD is the reflected wave front inclined at an angle r. As incident wave front and reflected wave front both are in the plane of paper, 1st law of reflection is proved.
To prove second law of reflection, consider ΔABC and ΔADC. BC = AD (by construction)
∠ABC = ∠ADC = 90° and AC is common. Therefore, the two triangles are congruent and, hence, ∠B AC = ∠DCA or ∠i = ∠r i.e., the angle of reflection is equal to the angle of incidence, which is the second law of reflection.
