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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 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 f₁ and f₂ will be

Options

  1. A1: 2
  2. B1: 3
  3. C3: 5
  4. D2: 3

Correct answer

B. 1: 3

Step-by-step solution

For case (1) aligned & 1.5 v₁ - 1 = (1.5-1) R₁ & 1 f₁ - 1.5 v₁ = 1-1.5 aligned 1 f₁ = (1.5-1) R₁ ...(1) 1 f₁ = 1 2 R₁ For case (2) aligned & 1.5 v₁ - 1.2 = (1.5-1.2) R₂ & 1.2 f₂ - 1.5 v₁ = (1.2-1.5) & 1.2 f₂ = 0.3 R₂ & 1 f₂ = 1 4 R₂ aligned So clearly, f₁ f₂ = 2 2 4 3 = 1 3

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