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An observer can see through a pinhole the top end of a thin rod of height h , placed as shown in the figure. The beaker height is 3 h and its radius h . When the beaker is filled with a liquid up to a height 2 h , he can see the lower end of the rod. Then the refractive index of the liquid is

Options

  1. A5 2
  2. B5 2
  3. C3 2
  4. D3 2

Correct answer

B. 5 2

Step-by-step solution

PQ = QR = 2 h      ∴   ∠ i = 4 5 0  ∴  ST = RT,   h = KM = MN So, KS = h 2 + 2 h 2 = h 5  ∴   sin  r = h h 5 = 1 5  ∴   μ =  sin i  sin r =  sin 45° 1 / 5 = 5 2

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