Question

When an object is placed at a distance of 15 cm from a concave mirror, its image is formed at 10 cm in front of the mirror. Calculate the focal length of the mirror.

Answer 1

Distance of the object from the mirror 'u' = −15 cm

Distance of the image 'v' = −10 cm
We have to find the focal length of the mirror 'f'.
Using the mirror formula, we get
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}+\frac{1}{u} \\ \frac{1}{f}=\frac{1}{-10}+\frac{1}{-15}=-\frac{1}{10}-\frac{1}{15} \\ \frac{1}{f}=-\frac{3}{30}-\frac{2}{30} \\ \frac{1}{f}=-\frac{5}{30} \\ f=-6\mathrm{cm} \end{gathered}$$

Thus, the focal length of the concave mirror 'f' is 6 cm.