Question

An object is kept at a distance of $60cm$ from a concave mirror. For getting a magnification of $\frac{1}{2}$, focal length of the concave mirror required is :

• A. $20cm$
• B. $40cm$
• C. $-20cm$
• D. $30cm$
• E. $10cm$

Answer 1

The correct option is C $-20cm$

Given, Magnification, $m=-\frac{v}{u}$

$\frac{1}{2}=-\frac{v}{60}$

$v=-30cm$

From lens formula, $\frac{1}{f}=\frac{1}{v}-\frac{1}{u}$

$\frac{1}{f}=\frac{1}{-30}+\frac{1}{-60}$

$\frac{1}{f}=-\frac{-2-1}{60}=\frac{-3}{60}$

$f=-20cm$