In figure, P is a point object placed at a distance r from a plane mirror M1M2. With P as centre and PO = r as radius, draw a spherical arc; AB. This is the spherical wavefront from the object, incident on M1M2.
If mirrors were not present, the position of wavefront AB would be A′B′ where PP′ = 2r. In the presence of the mirror, wave front AB would appear as A′′PB′′,
According to Huygen’s construction. As it is clear from the figure A′B′ and A′′B′′ are two spherical arcs located symmetrically on either side of M1M2.
Therefore, A′P′B′ can be treated as reflected image of A′′PB′′. From simple geometry, we find OP = OP′, which was to be proved