Question

A person standing in front of a mirror finds his image at a distance of $6m$ from himself. What is the distance of the person from the mirror?

Answer 1

Step 1: Given data:

The diagram for the given data is

The distance of image from object $=6m$

Step 2: Formula used:

$Dis\tan ceofobjectfrommirror=dis\tan ceofimagefrommirror$

Step 3: Calculations:

$$\begin{gathered} Dis\tan ceofobjectfromimage=dis\tan ceofobjectfrommirror+dis\tan ceofimagefrommirror \\ (Fromdiagram) \\ AA\text{'}=AC+A\text{'}C \\ ButAC=A\text{'}C \\ Thus,AA\text{'}=2AC \\ 6m=2\times AC \\ AC=\frac{6}{2} \\ =3m \\ AC=dis\tan cebetweenobjectandmirror=3m \end{gathered}$$

Thus, the distance between the person and mirror is 3m.