Question

Prove experimentally that images are formed as far behind in a plane mirror as the object is in front of it.

Answer 1

Consider an object ‘O’ situated in front of a plane mirror MM, A ray of light which starts from point ‘O’ perpendicularly, is reflected back along the same path (See the following figure).
However, another ray that moves along OB is reflected along with BC, obeying the laws of reflection, such that BN is normal. Produce OA and CB backward, such that they meet at a point I. Then ‘I’ is the image of ‘O’.

We have to prove that OA = IA

∠i = ∠r            [By the laws of reflection] ...(i)

Also, ∠i = ∠l    [Pair of alternate angles] ...(ii)

∠r = ∠2           [Pair of corresponding angles]

Comparing (i) and (ii), ∴ ∠l = ∠2

In ΔBAI and BAO

∠1 = ∠2         [Proved]

∠3 = ∠4         [Each = 90°]

BA = BA          [Common to both Δs]

∴ ΔBAI ≅ ΔBAO

Thus, in particular OA = IA.