Consider AB a plane incident wavefront on a mirror M1M2. Let ÐBAA' = Ði = be the angle of incidence. Every point on the wavefront AB is a source of secondary disturbance. Let the disturbance at B strike the mirror at A|. In a time t second when B reaches A|, the point A would have been reflected and will have traveled a distance of AB| such that AB|= BA| i.e.,
BA| = ct and AB| = ct. With A as centre, draw an arc of radius ct. Repeat for points D and others on AB. From A| draw a tangent to these arcs (dotted) as shown. A|B| therefore represents the reflected wavefront. To make sure A|B| is the reflected wavefront one should prove that
DP + PD| = BA|
Draw PN to BA|
DP = BN
In Ds ABA| and AA|B|
AA| is common
Also BA| = AB| = ct and so the triangles are congruent.
As PN is parallel to AB
PA| is common
these Ds are congruent.
NA| = PD|
DP + PD| = BN + NA| = BA|
A|B| is the true reflected wave front.
Further the wavefronts incident and reflected are perpendicular to the plane of paper as rays lie in the plane of paper.
