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

Explanation

GIVEN A is an object in front of mirror LM and B is its image. Let AB cut LM at T.
TO PROVE AT = BT.
PROOF We know that angle of incidence is equal to the angle of reflection.
`therefore" "anglei=angler rArr angleACN=angleDCN.`
In `DeltaACT and DeltaBCT`, we have
`angleATC=angleBTC=90^(@), CT = CT,`
`angleCAT=angleACN=i" "["alt. int. "angles]`
`angleCBT=r" "["corr. "angles]`
`therefore" "angleCAT=angleCBT" "[because i = r]`
`therefore" "DeltaACT~=DeltaBCT.`
Hence, AT = BT.`