An object placed $20cm$ in front of a mirror is found to have an image $15cm$ in front of it. Find the focal length and the kind of mirror used?

Step-1: Apply sign convention to write the given data

The distance of the object from the mirror is $u=-20cm$

The distance of the image formed from the mirror is $v=-15cm$

Let $f$ be the focal length of the given mirror.

Step-2: Apply mirror formula to find $f$

The mirror formula is given by $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}$

Now substitute all the required values in the above formula, we have

$$\begin{gathered} \Rightarrow \frac{1}{f}=\frac{1}{-15}+\frac{1}{-20} \\ \Rightarrow \frac{1}{f}=-\frac{7}{60} \\ \Rightarrow f=-\frac{60}{7}cm \end{gathered}$$

The focal length of the mirror is $\frac{60}{7}cm$ and the negative sign indicates that the mirror is concave mirror.