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JEE Main201815 Apr 2018Morning ShiftPhysicsRay OpticsActual

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

Options

  1. A1.50
  2. B1.55
  3. C1.75
  4. D1.51

Correct answer

B. 1.55

Step-by-step solution

Case-1 1 f₁ = ( -1 R ) f =-28 P =2 P ₁+ P ₂ 1 28 =2 ( -1 R ) ( . Power, .P= 1 f & f_ plane mirror = ) Case-2 1 f₁ = ( -1 R ) f₂=- R 2 f=-10 ~cm P =2 P ₁+ P ₂ 1 10 =2 ( -1 2 )+ 2 R or, 1 10 = 1 28 + 2 R 2 R = 1 10 - 2 28 = 18 280 or, R = 280 9 ~cm or, 1 28 =2 ( -1 280 ) 9 -1= 5 9 =1+ 5 9 = 14 9 =1.55

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