Question

If a man's face is $25\text{cm}$ in front of a shaving mirror, it produces an erect image $1.5$ times the size of the face, the focal length of the mirror is -

• A. $75\text{cm}$
• B. $25\text{cm}$
• C. $15\text{cm}$
• D. $60\text{cm}$

Answer 1

The correct option is A $75\text{cm}$

Given :
$u=-25\text{cm}$
$m=1.5$

We know that,

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

$\Rightarrow 1.5=\frac{-v}{-25}$

$\Rightarrow v=37.5\text{cm}$

Applying mirror formula,

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

$\Rightarrow \frac{1}{f}=\frac{1}{37.5}+\frac{1}{(-25)}$

$\Rightarrow f=-75\text{cm}$

Hence, option $\left(A\right)$ is the correct answer.