JEE Main · 2023 · 01 Feb 2023 · Shift 2 · Geometrical Optics

The focal length of the concave mirror is $f=\frac{R}{2}=20$ cm, taken as $f=-20$ cm. For the object at $u=-15$ cm, $\frac{1}{v}=\frac{1}{f}-\frac{1}{u}=-\frac{1}{20}+\frac{1}{15}=\frac{1}{60}$, so $v=+60$ cm, a virtual image $60$ cm behind the mirror since the object lies inside the focus. For the object at $u=-25$ cm, $\frac{1}{v}=-\frac{1}{20}+\frac{1}{25}=-\frac{1}{100}$, so $v=-100$ cm, a real image $100$ cm in front of the mirror. With one image $60$ cm behind the pole and the other $100$ cm in front, the separation between the two images is $60+100=160$ cm.