Question

A concave mirror has a focal length of 20 cm. Find the position or positions of an object for which the image-size is double of the object size.

• A. 30cm, 30cm
• B. 10cm, 20cm
• C. 10cm, 10cm
• D. 10cm, 30cm

Answer 1

The correct option is D

10cm, 30cm

For the concave mirror, f = -20 cm, M = $\frac{-v}{u}=2$
v = -2u
$1stcase\frac{1}{v}+\frac{1}{u}=\frac{1}{f}$
$\frac{1}{2u}+\frac{1}{-u}=\frac{1}{-f}$
$u=\frac{f}{2}=10cm$
$2ndcase$
$\frac{1}{-2u}+\frac{1}{-u}=\frac{1}{-f}$
$u=\frac{3f}{2}=30cm$
$\therefore$ The positions are 10 cm or 30 cm from the concave mirror.