When a thin convergent glass lens ( μ g = 1.5 ) and has power of +5 D is immersed in a liquid of refractive index μ ℓ it acts as a divergent lens of focal length 100 cm . Then μ ℓ is :

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When a thin convergent glass lens ( μ g ​ = 1.5 ) and has power of +5 D is immersed in a liquid of refractive index μ ℓ ​ it acts as a divergent lens of focal length 100 cm . Then μ ℓ ​ is :

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Ans (B) For 1 s t case, f = 5 1 ​ m = 20 cm ∴ ( μ g ​ − 1 ) [ R 1 ​ 1 ​ − R 2 ​ 1 ​ ] = 20 1 ​ ⇒ [ R 1 ​ 1 ​ − R 2 ​ 1 ​ ] = 20 1 ​ × 0.5 1 ​ = 10 1 ​ For 2 n d case, ( μ ℓ ​ μ g ​ ​ − 1 ) [ R 1 ​ 1 ​ − R 2 ​ 1 ​ ] = − 100 1 ​ ⇒ ( μ ℓ ​ μ g ​ ​ − 1 ) = − 100 1 ​ × 10 ⇒ μ ℓ ​ μ g ​ ​ = 1 − 10 1 ​ = 10 9 ​ ∴ μ ℓ ​ = 3 5 ​

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