A planoconvex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the

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A planoconvex lens becomes an optical system of $28 cm$ focal length when its plane surface is silvered and illuminated from left to right as shown in Fig-A. If the same lens is instead silvered on the curved surface and illuminated from other side as in Fig. B, it acts like an optical system of focal length $10 cm$ . The refractive index of the material of lens is

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Case-1 f 1 ​ 1 ​ = ( R μ − 1 ​ ) f = − 28 P = 2 P 1 ​ + P 2 ​ ⇒ 28 1 ​ = 2 ( R μ − 1 ​ ) ( ∵ Power, P = f 1 ​ & f plane mirror ​ = ∞ ) Case-2 f 1 ​ 1 ​ = ( R μ − 1 ​ ) f 2 ​ = − 2 R ​ f = − 10 cm P = 2 P 1 ​ + P 2 ​ ⇒ 10 1 ​ = 2 ( 2 μ − 1 ​ ) + R 2 ​ or, 10 1 ​ = 28 1 ​ + R 2 ​ ⇒ R 2 ​ = 10 1 ​ − 28 2 ​ = 280 18 ​ or, R = 9 280 ​ cm or, 28 1 ​ = 2 ( 280 μ − 1 ​ ) 9 ⇒ μ − 1 = 9 5 ​ ∴ μ = 1 + 9 5 ​ = 9 14 ​ = 1.55

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