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  • The image of an object placed at a point A before a plane mirror LM is seen at the point B by an observer at D as shown in Figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

The image of an object placed at point A before a plane mirror LM is seen at point B by an observer at D as shown in Figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.

Answers (1)

Given: ABC is a triangle and let C be a point on AB.

To prove: CA = CB

Proof: Since i and r are the angle of incidence and reflection respectively.

CN is normal then

\angleLCA = 90 – i, \angleMCD = 90 – r

\because \angleACN = \angleDCN = i = r                              (Given)

\Rightarrow \angleLCA = \angleMCD = 90 – i = 90 – r             (Since, i = r )

\Rightarrow \angleBCL = 90 – r                                           (vertically opposite angles)

\because \angleBCL = \angleLCA

\angleL bisects BA

Hence, CB = CA,

Hence, proved.

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