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A concave mirror for face viewing has focal length of $0.4 m.$ The distance at which you hold the mirror from your face in order to see your image upright with a magnification of $5$ is :
Option 1)
$0.24\: m$
Option 2)
$1.60\: m$
Option 3)
$0.32\: m$
Option 4)
$0.16\: m$

Answers (1)

best_answer

$\frac{1}{v}-\frac{1}{u}=\frac{1}{f} \: \: \:\; \Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u}$

$m=\frac{v}{u}$

$\frac{1}{m}=\frac{u}{v}$

$\frac{1}{m}=u\left [ \frac{1}{f}+\frac{1}{u} \right ]$

$\frac{1}{m}=\frac{u}{f}+1$

$u=f\left ( 1-\frac{1}{m} \right )$

$u=f\left ( 1-\frac{1}{m} \right )$

$u=\left ( 0.4 \right )\left ( 1-\frac{1}{5} \right )$

$u=\left ( 0.4 \right )\left ( .8 \right )$

$u=.32\; m$

Option 1)

$0.24\: m$

Option 2)

$1.60\: m$

Option 3)
$0.32\: m$
Option 4)

$0.16\: m$

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