CBSE Class 10 Science 2017 · Paper 31/1/1/C · Question 10

Magnification: the magnification produced by a spherical mirror is the ratio of the height of the image ($h^{\prime }$) to the height of the object ($h$), $m=\frac{h^{\prime }}{h}=-\frac{v}{u}$. It tells how many times the image is magnified compared with the object. Focal length: $u=-20$ cm and, since the real image is formed in front of the mirror, $v=-40$ cm. Then $\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=-\frac{1}{40}-\frac{1}{20}=-\frac{3}{40}$, so $f=-\frac{40}{3}$ cm $\approx -13.3$ cm. The focal length of the concave mirror is about $13.3$ cm (negative by the sign convention).