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AP EAMCET2002PhysicsRay Optics

A convex lens of focal length 0.15 ~m is made of a material of refractive index 3 2 . When it is placed in a liquid, its focal length is increased by 0.225 ~m . The refractive index of the liquid is

Options

  1. A7 4
  2. B5 4
  3. C9 4
  4. D3 2

Correct answer

B. 5 4

Step-by-step solution

f_a=0.15 ~m , _g=3 / 2, f_e=0.225+0.15 From lens formula, For air, 1 f_a = ( _g _a -1 ) ( 1 R₁ - 1 R₂ ) For liquid, 1 f_l = ( _g _l -1 ) ( 1 R₁ - 1 R₂ ) aligned 1 / f_a 1 / f_l & = ( _g / _a-1 ) ( _g _l -1 ) f_l f_a & = ( 3 / 2 1 -1 ) ( 3 / 2 _l -1 ) 0.375 0.15 & = 1 / 2 ( 3 2 _l -1 ) ( 3 2 _l -1 ) & = 1 / 2 5 / 2 3 2 _l -1 & = 1 5 3 2 _l & = 1 5 +1 3 2 _l = 6 5 _l & = 5 4 aligned

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