Question

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. "

Answer 1

see figure, P is a point object placed at a distance r from the plane mirror. if we assume P as centre then, PO = r as radius, draw a spherical arc AB. this is the spherical wavefront from the object, incident on plane mirror.

if mirror is not present, the position of wavefront AB would be A'B' . where PP' = 2r. in the presence of the mirror, wavefront AB would appear as A"B".

now according to Huygen's construction.

as it is clear from A'B' and A"B" are two spherical arcs located symmetrically on either side of plane mirror.

There, A'B' can be treated as reflected image of A"B".

distance between P and P' = 2r

PP' = 2r

or, OP + OP' = 2r

or, r + OP' = 2r

or, OP' = r

so, OP = OP'

hence, object distance from the mirror = image distance from the mirror.

hence proved.

also read : For sound waves, the Doppler formula for frequency shift differs slightly between the two situations (i) source at rest;...

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