Question 13: NCERT Solutions for 12th Class Physics: Chapter 10-Wave Optics
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 distance of the object from the mirror.
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 wave front from the object, incident on M1M2 If mirrors were not present, the position of wave front AB would be A’B’ where PP’ = 2r. In the presence of the mirror, wave front A B 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.
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NCERT Solutions for 12th Class Physics: Chapter 10-Wave Optics