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COMEDK2015PhysicsRay Optics

All lights are switched off, except for a bright point-light source kept at the bottom of a swimming pool filled with clear water of refractive index 4 / 3 . As a result, only a circular patch of 6 ~m diameter of the water surface is visible to spectators standing around the swimming pool. Which of the following gives the nearest value of the depth of the pool?

Options

  1. A1.6 ~m
  2. B2.0 ~m
  3. C2.6 ~m
  4. D3.0 ~m

Correct answer

C. 2.6 ~m

Step-by-step solution

For the given situation, the ray diagram is shown below. Refractive index of water, _ w = 4 3 r= D 2 = 6 2 =3 ~m The given situation is possible only for the case of total internal reflection. If i_ C be the critical angle, then i_ C = 1 _ w i_ C = 1 4 / 3 i_ C = 3 4 r r²+h² = 3 4 [ i_ C = r r²+h² ] 3 3²+h² = 3 4 9+h²=16 h²=7, h= 7 =2.6 ~m

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