# You have learnt in the text how Huygen's principle leads to the laws of reflection and refraction. Use the same principle

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You have learnt in the text how Huygen's 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.

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Consider that a point object O is placed in front of a plane mirror x y and a spherical wavefront APB originating from the object is incident on the mirror as shown in figure The lines OA, OP and OB (normal to the incident wavefront APB at the points A’ P
and B) represent the incident rays. Since the distance OP is smaller than OA’ or OB’ > the disturbance will reach the point P earlier than it reaches the points A’ and B’ on the mirror.

Therefore, the instant, when the disturbance reaches the points A’ and B’ > the secondary wavelet from the point P will grow into a sphere of radius (OA’ – OP) or (OB’ – OP). At this instant, the points A’ and B’ on the mirror have just become the sources of secondary wavelets and therefore, the secondary wavelets originating from these points will be of zero radius at that instant.

To find the reflected wave front (new position of the wave front after reflection from the plane mirror); with the point P as centre, draw a sphere of radius PP’ = (OA’ - OP) or (OB’ - OP). Then, the sphere A’ P’ B’, the common envelope of the secondary wavelets issuing out from the points A’, P’ and B’ gives the reflected wave front (diverging) and the lines IAS IP’ and jB’ normals to the reflected wave front represent the reflected rays. The point I, from which the reflected wave front appears to come from, is the virtual image of the object O From simple geometry,
IP = OP
i..e, image is formed as for behind the plane mirror as the object is in front of it.