A concave lens produces an image 20 cm from the lens of an object placed 30 cm from the lens. The focal length of the lens is:(a) 50 cm (b) 40 cm (c) 60 cm (d) 30 cm

(c) 60 cm

Explanation

Given:

Object distance from the lens, $u$ = $-$30 cm

Image distance from the lens, $v$ = $-$20 cm

To find: Focal length of the lens, $f$.

Solution:

From the lens formula, we know that-

$\frac {1}{v}-\frac {1}{u}=\frac {1}{f}$

Substituting the given values in the formula, we get-

$\frac {1}{(-20)}-\frac {1}{(-30)}=\frac {1}{f}$

$-\frac {1}{20}+\frac {1}{30}=\frac {1}{f}$

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

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

$f=-60cm$

Thus, the focal length of the lens is 60cm.