A man uses a concave mirror for shaving. He keeps his face at a distance of $25 c m$ 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

$u = - 25 c m$
$m = \frac{A^{'} B^{'}}{A B} = - \frac{v}{u} \Rightarrow 1.4 = - (\frac{v}{- 25}) \Rightarrow \frac{14}{10} = \frac{v}{25}$ '
$\Rightarrow v = \frac{25 \times 14}{10} = 35 c m$
Now, $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$
$\Rightarrow \frac{1}{f} = \frac{1}{35} - (\frac{1}{- 25}) = \frac{5 - 7}{175} = - \frac{2}{175} \Rightarrow f = - 87.5 c m$
So, focal length of the concave mirror is $87.5 c m$ .

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

u=−25cmm=A′B′AB=−vu⇒1.4=−(v−25)⇒1410=v25'⇒v=25×1410=35cmNow, 1v+1u=1f⇒1f=135−(1−25)=5−7175=−2175⇒f=−87.5cmSo, focal length of the concave mirror is 87.5cm.

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