Question

You have learnt in the text how Huygens’ principle leads to 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.

Answer 1

To prove, let us take the point object on the centre and draw a circle so that it touches the mirror. We can consider it as the plane section of the spherical wavefront from the point object that has just touched the mirror. Now again draw the position of the same wavefront after certain time say t in the presence and in the absence of the plane mirror. Hence we obtain two symmetrically located arcs on either side of the mirror. Then we can easily find using simple geometry that the image of the object (i.e. centre of reflected wavefront), lies at the same distance from the mirror as the object is situated from the mirror.