##### 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.

Huygens principle is used to explain phenomena such as refraction, reflection and diffraction by describing the light to travel forward in the form of wave fronts. These primary wave fronts act as source for the next secondary one in the propagation of light.

We start by supposing that an object O placed in front of a plane mirror MP at a distance equal to the radius of the circle (as shown in the figure below)

A circle is drawn from the centre taken as object O such that the plane mirror is just tangent to the circle at the point P. The Huygens’s Principle thus points that AB is the first wave front of the incident light from the object O.

If we suppose the absence of the mirror, then by Huygens principle a similar wave front can be drawn parallel to AB behind the P at a distance of the same radius of the circle (as given in the figure below).

A’B’ can be considered as a virtual reflected ray for the plane mirror. Therefore, a point object placed in front of the plane mirror produces a virtual image whose distance from the mirror is equal to the object at an equal distance. Further another secondary wave front can be drawn by taking the circle A’B’ and placing a mirror tangent to the circle and parallel to the previous one. The point ‘P’ will act as an object for the next virtual image. The secondary wave fronts thus are at a distance of the radius of the circle from the tangent of a virtual plane mirror.

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