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A hemispherical vessel is completely filled with a liquid of refractive index . A small coin is kept at the lowest point ( O ) of the vessel as shown in figure. The minimum value of the refractive index of the liquid so that a person can see the coin from point E (at the level of the vessel) is

Options

  1. A3
  2. B3 2
  3. C3 2
  4. D2

Correct answer

D. 2

Step-by-step solution

For the rays from coin to reach the point E , the refracted rays must grazing the surface, i.e. they must be incident at critical angle _c inside the liquid. = 1 _c is minimum when _c is maximum. Maximum value of _c=45^ has a minimum value of 2 .

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