Question

A man standing in front of a concave spherical mirror of radius of curvature 120 cm sees an erect image of his face four times its natural its natural size. Then the distance of the man from the mirror is -

• A. $180cm$
• B. $300cm$
• C. $240cm$
• D. $45cm$

Answer 1

The correct option is A $180cm$

Radius of curvature (r) = 120 cm

Magnification = 4

Focal length (f) = $\frac{r}{2}$

$\Rightarrow f=\frac{120}{2}=60\text{cm}$

Magnification (m)$=-\frac{v}{u}=4$

$\Rightarrow v=-4u$ ……(1)

From the mirror formula,

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

Substituting the value of v from equation (1),

$\frac{1}{60}=\frac{1}{u}+\frac{1}{-4u}$

$\frac{3}{4u}=\frac{1}{60}$

$4u=180$

$u=45\text{cm}$

From equation (1)

$v=-4u$

$v=-4\left(45\right)=-180\text{cm}$

The distance of the man from the mirror is 180 cm