Q 12-09-092JEE MainJEE Main 2024 (29 Jan, Shift 1)Easy
A convex mirror of radius of curvature $30\ \text{cm}$ forms an image that is half the size of the object. The object distance is:
Answer: (C) $-15\ \text{cm}$
$f = +15\ \text{cm}$. A convex mirror forms a virtual erect image, so $m = -\dfrac vu = \dfrac12 \Rightarrow v = -\dfrac u2$.
$$\frac1v + \frac1u = \frac1f \;\Rightarrow\; -\frac2u + \frac1u = \frac1{15} \;\Rightarrow\; u = -15\ \text{cm}$$
Solution by Sreeraj P, M.Sc Physics