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

u = -25 cm

$m = \frac{A_{1} B_{1}}{A B} = \frac{u}{v}$

$\Rightarrow 1.4 = - \frac{(v)}{- 25}$

$\Rightarrow \frac{14}{10} = \frac{v}{25}$

$\Rightarrow v = \frac{25 \times 14}{10} = 35 cm$

Now, $\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$

$\Rightarrow \frac{1}{f} = \frac{1}{35} - \frac{1}{25}$

$= \frac{5 - 7}{175} = - \frac{2}{175}$

$\Rightarrow f = - 87.5$

So, focal length of the concave mirror is 87.5 cm.

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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.

u = -25 cm m=A1B1AB=uv ⇒1.4=−(v)−25 ⇒1410=v25 ⇒v=25×1410=35 cm Now, 1f=1v+1u ⇒1f=135−125 =5−7175=−2175 ⇒f=−87.5 So, focal length of the concave mirror is 87.5 cm.