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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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