Reflection & Mirrors question from JEE Main 2025 (7 Apr, Shift 2)

Answer: (c)

1. Erect diminished image ($m = \frac{1}{4}$) means a convex mirror: $u = -x$, $v = +\frac{x}{4}$.
2. Object-image distance: $x + \frac{x}{4} = 40 \Rightarrow x = 32\text{ cm}$, $v = 8\text{ cm}$
3. $\frac{1}{f} = \frac{1}{v} + \frac{1}{u} = \frac{1}{8} - \frac{1}{32} = \frac{3}{32} \Rightarrow f = 10.67\text{ cm}$
4. (Taking $m = -\frac{1}{4}$ with a concave mirror also gives $|f| = 10.7$ cm.) So the answer is (c) 10.7 cm.