List-I gives different lens configurations. The radius of curvature of each curved surface is R . Parallel paraxial rays of light parallel to the axis of lens traversing through the lens get focused a

Question

List-I gives different lens configurations. The radius of curvature of each curved surface is $R$ . Parallel paraxial rays of light parallel to the axis of lens traversing through the lens get focused at distance $f$ from the lens. List-II gives corresponding values of $f$ . ( $μ$ represent refractive index of medium)

List - I	List - II
(P)	(1) $13 R$
(Q) Lens is silvered	(2) $\frac{13 R}{4}$
(R) Plano concave lens	(3) $\frac{7 R}{3}$
(S)	(4) $\frac{7 R}{16}$
	(5) $R$

TestHub · Accepted Answer

( P ) Two-surface refraction: v 1 ​ 1.5 ​ = R 0.5 ​ ⇒ v 1 ​ = 3 R , then v 1.4 ​ − 3 R 1.5 ​ = R 0.1 ​ , so f = 3 7 R ​ (P to 3). ( Q ) Lens is silvered: P e q ​ = 2 P l e n s ​ + P mi rror ​ = R 2 ( 0.1 ) ​ + R 3 ​ = R 3.2 ​ , so f = 3.2 1.4 ​ R = 16 7 R ​ (Q to 4). ( R ) Plano concave lens: v 1.3 ​ = − R 1.3 − 1.2 ​ , so ∣ f ∣ = 13 R (R to 1). ( S ) Combination in the medium: f 1 ​ = f 1 ​ 1 ​ + f 2 ​ 1 ​ = 13 R 4 ​ , so f = 4 13 R ​ (S to 2). Answer (D).

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