A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of f₁ in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of f₂ when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5, the ratio of f₁ and f₂ will be (a) 2: 3 (b) 1: 3 (c) 1: 2 (d) 3: 5

Answer: (b). Plano-convex in air: 1/f₁ = 0.5/2 ⇒ f₁ = 4 cm. Second lens in liquid: 1/f₂ = ((1.5)/(1.2) - 1)1/3 = 0.25/3 ⇒ f₂ = 12 cm. f₁: f₂ = 4: 12 So the answer is (b) 1: 3.

A plano-convex lens having radius of curvature of first surface 2 cm… | JEE Main 2025 (24 Jan, Shift 1)

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Spherical Surfaces & Thin Lenses

A plano-convex lens having radius of curvature of first surface 2 cm exhibits focal length of $f_1$ in air. Another plano-convex lens with first surface radius of curvature 3 cm has focal length of $f_2$ when it is immersed in a liquid of refractive index 1.2. If both the lenses are made of same glass of refractive index 1.5, the ratio of $f_1$ and $f_2$ will be

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Answer: (b)

Plano-convex in air: $\frac{1}{f_1} = \frac{0.5}{2} \Rightarrow f_1 = 4$ cm.
Second lens in liquid: $\frac{1}{f_2} = \left(\frac{1.5}{1.2} - 1\right)\frac{1}{3} = \frac{0.25}{3} \Rightarrow f_2 = 12$ cm.
$f_1 : f_2 = 4 : 12$
So the answer is (b) $1 : 3$ .

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