Spherical Surfaces & Thin Lenses question from JEE Main 2025 (2 Apr, Shift 1)

Answer: (c)

1. Point A: $u = -30$, $f = 20 \Rightarrow v = 60$ cm, on the axis.
2. Point B: $u = -29$ cm, height 2 cm: $\frac{1}{v} = \frac{1}{20} - \frac{1}{29} \Rightarrow v \approx 64.4$ cm, $m = -\frac{64.4}{29} \approx -2.22$, height $\approx -4.4$ cm.
3. Image A'B': $\Delta x \approx 4.4$ cm, $\Delta y \approx -4.4$ cm (roughly: $\Delta x = m^2 \times 1 = 4$, $\Delta y = -2 \times 2 = -4$).
4. $\tan\theta = -1 \Rightarrow \theta = -45^\circ$. So the answer is (c).