Question

A real image of half the size is obtained in a concave spherical mirror with a radius of curvature of $40cm$, the distance of object and its image will be

• A. $30cmand60cm$
• B. $60cmand30cm$
• C. $15cmand30cm$
• D. $30cmand15cm$

Answer 1

Answer: (B)

$60cmand30cm$

Lets, $u=$ object distance

$v=$ image distance

Given,

$R=40cm$

$f=\frac{R}{2}=20cm$

magnification, $m=\frac{h}{2h}=\frac{v}{u}$ (for real image)

$v=\frac{u}{2}$. . . . (1)

By mirror formula,

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

$\frac{1}{20}=\frac{2}{u}+\frac{1}{u}$

$u=60cm$

From equation (1),

$v=\frac{60}{2}=30cm$

The correct option is B.