Question

An object 2 cm high is placed at a distance of 16 cm from a concave mirror, which produces a real image 3 cm high. What is the focal length of the mirror ?

• A. -9.6 cm
• B. -3.6 cm
• C. -6.3 cm
• D. -8.3 cm

Answer 1

The correct option is A -9.6 cm

Here $h_1$ = 2 cm, u = -16 cm, $h_2$ = -3 cm (Since image is real and inverted.)
$\because m=\frac{h_2}{h_1}=-\frac{v}{u}\therefore v=\frac{-h_2}{h_1}u=\frac{3}{2}\times (-16)=-24cm$
$\frac{1}{f}=\frac{1}{v}+\frac{1}{u}=-\frac{1}{24}-\frac{1}{16}=\frac{-2-3}{48}=\frac{-5}{48};f=\frac{-48}{5}=-9.6cm$