You have learnt in the text how Huygens’ principle leads to the laws of reflection and refraction. Use the same principle to deduce directly that a point object placed in front of a plane mirror produces a virtual image whose distance from the mirror is equal to the object distance from the mirror.

Explanation

In Fig. P is a point object placed at a distance `r` from a plane mirror `M_(1), M_(2)`. With `P` as centre and `PO = r` as radius, draw a spherical arc , `AB`. This is the spherical wavefront from the object, incident on `M_(1),M_(2)`.
If mirror were not present, the position of wave front `AB` would appear as `P"B"`, according to huyghen's construction. As is clear from the figure, `A'B'` and `A"B"` are two spherical arcs located symmetrically on either side of `M_(1) M_(2)`. Therefore, `A'PB'` can be treated as reflected image of `A"PB"`. From simple geometry, we find `OP = OP'`. which was to be proved.