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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.
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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