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A convex lens has a certain focal length in air. When it is completely immersed in a transparent liquid of refractive index 4 3 , its focal length becomes 4 times its focal length in air. The refractive index of the material of the lens is:

Options

  1. A13 9
  2. B8 5
  3. C5 3
  4. D3 2

Correct answer

D. 3 2

Step-by-step solution

Let the focal length of the lens in air be f_a and in the liquid be f_m . By the lens maker's formula in air: 1 f_a = ( _L - 1) ( 1 R₁ - 1 R₂ ) When immersed in the liquid of refractive index _m : 1 f_m = ( _L _m - 1 ) ( 1 R₁ - 1 R₂ ) Dividing the two equations: f_m f_a = _L - 1 _L _m - 1 Given that f_m = 4f_a and _m = 4 3 : 4 = _L - 1 3 _L 4 - 1 4 ( 3 _L 4 - 1 ) = _L - 1 3 _L - 4 = _L - 1 2 _L = 3 _L = 3 2 Answer: 3 2

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