Q 12-09-094JEE MainJEE Main 2024 (29 Jan, Shift 2)Medium
If the distance between an object and its two times magnified virtual image produced by a curved mirror is $15\ \text{cm}$, the focal length of the mirror must be:
Answer: (C) $-10\ \text{cm}$
A magnified virtual image is formed by a concave mirror. $m = -\dfrac vu = 2 \Rightarrow v = -2u$.
With $u$ negative, the image is behind the mirror, and the object–image distance is
$$v - u = -3u = 15 \;\Rightarrow\; u = -5\ \text{cm},\ v = 10\ \text{cm}$$
$$\frac1f = \frac1v + \frac1u = \frac1{10} - \frac15 = -\frac1{10} \;\Rightarrow\; f = -10\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics