Siddharth wanted to see his inverted image in a plane mirror. So, he stood between a concave mirror and a plane mirror facing each other as shown in the figure. Knowing the focal length of the concave mirror, he found the distance between him and his inverted virtual image, formed in the plane mirror. What is his answer?

Step 1: Given data

Focal length $f=-2$m

Object distance $u=-3$m

Step 2: Finding the image distance:

Using the mirror formula, $\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$$\begin{gathered} \frac{1}{-2}=\frac{1}{-3}+\frac{1}{v} \\ -\frac{1}{2}+\frac{1}{3}=\frac{1}{v} \\ \frac{1}{v}=\frac{1}{6} \end{gathered}$$

$v=6$m

An inverted, magnified and real image is formed at $6$m from the concave mirror which acts as an object to the plane mirror.

$\Rightarrow$The inverted virtual image is formed at a distance of $5+3-6=2$m behind the plane mirror.

$\Rightarrow$The distance between the object and its virtual inverted image is $2+5=7$m.

Hence, the distance between him and his inverted virtual image, formed in the plane mirror is $7$m.