Question

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 Fig. Prove that the image is as far behind the mirror as the object is in front of the mirror.

Answer 1

Angle of incidence = Angle of reflection

$\Rightarrow \angle i=\angle r$...(1)

$AB\parallel NC$ [Both are perpendicular to LM]

$\Rightarrow \angle CAT=\angle ACN=\angle i$...(2)[Alternate angles]

$\angle CBA=\angle DCN=\angle r$...(3)[Corresponding angles]

From(1),(2) and (3) we get

$\angle CAT=\angle CBA$...(4)

In $△CAT$ and $△CBT$,

$\angle CAT=\angle CBT$...[From 4]

$\angle ATC=\angle BTC...\left[Each{90}^{\circ }\right]$

$CT=CT$...[Common side]

$\therefore △CAT\cong △CBT$..[AAS rule]

$\Rightarrow AT=BT$....[CPCT]

Hence proved.