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Question
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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