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# When an object is placed at a distance of 15 cm from a concave mirror, its image is formed at 10 cm in front of the mirror. Calculate the focal length of the mirror.

**Given:**

Distance of the object from the mirror $u$ = $-$15 cm

Distance of the image from the mirror $v$ = $-$10 cm

**To find: **The focal length of the mirror $f$.

**Solution:**

From the mirror formula, we know that-

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

Substituting the given values in the mirror formula we get-

$\frac{1}{f}=\frac{1}{(-10)}+\frac{1}{(-15)}$

$\frac{1}{f}=-\frac{1}{10}-\frac{1}{15}$

$\frac{1}{f}=\frac{-3-2}{30}$

$\frac{1}{f}=\frac{-5}{30}$

$\frac{1}{f}=-\frac{1}{6}$

$\frac{1}{f}=-\frac{1}{6}$

$f=--6cm$

Thus, the focal length $f$ of the concave mirror is **6 cm, **and the minus sign implies that the focus is on the front of the mirror (in the left).

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