Sum

A man uses a concave mirror for shaving. He keeps his face at a distance of 25 cm from the mirror and gets an image which is 1.4 times enlarged. Find the focal length of the mirror.

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#### Solution

Given,

Distance of the man's face (here, taken as object), *u* = −25 cm

According to the question, magnification, *m* = 1.4

\[m = \frac{A'B'}{AB} = - \frac{v}{u}\]

\[ \Rightarrow 1 . 4 = - \frac{(v)}{- 25}\]

\[\Rightarrow\frac{14}{10}=\frac{v}{25}\]

\[\Rightarrow v=\frac{25 \times 14}{10}=35 \text{ cm }\]

Using equation of mirror, we get:

\[\frac{1}{f} = \frac{1}{v} + \frac{1}{u}\]

`⇒ 1/f = 1/35 - 1/25`

\[= \frac{5 - 7}{175} = - \frac{2}{175}\]

⇒ *f* = −87.5

Hence, the required focal length of the concave mirror is 87.5 cm.

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