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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.

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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.

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u = -15 cm, v = -10 cm, f = ?

We know that

\(\frac{1}{v}\) + \(\frac{1}{u}\) = \(\frac{1}{f}\)

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

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

⇒ \(\frac{-3 - 2}{30}\) = \(-\frac{5}{30}\) 

= \(-\frac{1}{6}\)

f = -6 cm

The focal length of the concave mirror is 6 cm

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