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# 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.**

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