A spherical interface whose radius is R = 20 cm separates the two media, I and II as shown in the figure. The refractive index of medium I is μ 1 and that of medium II is μ 2 . Now match the list

Question

A spherical interface whose radius is R = 20 cm separates the two media, I and II as shown in the figure. The refractive index of medium I is μ 1 ​ and that of medium II is μ 2 ​ . Now match the list - I with list - II [Consider the pole 'O' as the origin and principal axis as the X-axis] List - I List - II (P) μ 2 ​ = 2 , μ 1 ​ = 1 , object distance u = − 10 cm (1) v = − 40 cm (Q) μ 2 ​ = 2 , μ 1 ​ = 1 , object distance u = − 20 cm (2) v = − 10 cm (R) μ 2 ​ = 1 , μ 1 ​ = 2 , object distance u = − 40 cm (3) v = 40 cm (S) μ 2 ​ = 1 , μ 1 ​ = 2 , object distance u = − 60 cm (4) v = − 12 cm (5) v = ∞

TestHub · Accepted Answer

v μ 2 ​ ​ − u μ 1 ​ ​ = R μ 2 ​ − μ 1 ​ ​ , with R = + 20 cm (P) v 2 ​ + 10 1 ​ = 20 1 ​ ⇒ v = − 40 cm → ( 1 ) (Q) v 2 ​ + 20 1 ​ = 20 1 ​ ⇒ v = ∞ → ( 5 ) (R) v 1 ​ + 40 2 ​ = − 20 1 ​ ⇒ v = − 10 cm → ( 2 ) (S) v 1 ​ + 60 2 ​ = − 20 1 ​ ⇒ v = − 12 cm → ( 4 ) Hence (B).

List - I	List - II
(P) $μ_{2} = 2, μ_{1} = 1$ , object distance $u = - 10 cm$	(1) $v = - 40 cm$
(Q) $μ_{2} = 2, μ_{1} = 1$ , object distance $u = - 20 cm$	(2) $v = - 10 cm$
(R) $μ_{2} = 1, μ_{1} = 2$ , object distance $u = - 40 cm$	(3) $v = 40 cm$
(S) $μ_{2} = 1, μ_{1} = 2$ , object distance $u = - 60 cm$	(4) $v = - 12 cm$
	(5) $v = \infty$

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