A concave-convex lens of refractive index 1.5 and the radii of… | JEE Main 2025 (8 Apr, Shift 2)

Q21JEE Main 2025 · 8 APR · SHIFT 2Difficult

Combination of Lenses

A concave-convex lens of refractive index 1.5 and the radii of curvature of its surfaces are 30 cm and 20 cm, respectively. The concave surface is upwards and is filled with a liquid of refractive index 1.3. The focal length of the liquid-glass combination will be

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Answer: (b)

Converging meniscus: convex surface $R = 20\text{ cm}$ , concave surface $R = 30\text{ cm}$ .
Glass: $P_g = 0.5\left(\frac{1}{20} - \frac{1}{30}\right) = \frac{1}{120}$
Liquid in the concave side is plano-convex: $P_l = \frac{0.3}{30} = \frac{1}{100}$
$P = \frac{1}{120} + \frac{1}{100} = \frac{11}{600} \Rightarrow f = \frac{600}{11}\text{ cm}$
So the answer is (b) $\frac{600}{11}$ cm.

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