Question

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

• A. 15 cm, 30 cm
• B. 30 cm, 15 cm
• C. 30 cm, 60 cm
• D. 60 cm, 30 cm

Answer 1

The correct option is D

60 cm, 30 cm

Image must be real
$m=\frac{-v}{u}=-\frac{1}{2}\Rightarrow \frac{v}{u}=\frac{1}{2}\Rightarrow v=\frac{u}{2}$
$\Rightarrow \frac{1}{v}+\frac{1}{v}=\frac{1}{f}\Rightarrow \frac{1}{u}+\frac{2}{u}=-\frac{1}{20}[\because f=\frac{R}{2}]$
$\Rightarrow \frac{1+2}{u}=-\frac{1}{20}\Rightarrow u=-60cm$
$\therefore v=-30cm$ where v is the image distance, u is the object distance and m is the magnification.