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A transparent solid sphere of radius 2 cm and density rho floats in a transparent liquid of density 2 rho kept in a beaker. The bottom of the beaker is spherical in shape with its radius of anvature 8 cm and is silvered to make it a concave mirror as shown in Fig. When an abject is placed at a distance of 10 cm directly above the centre of the sphere its final image coincide with it. If ' h ' is the height of liquid surface from the apex of the bottom as shown in figure. Consider paraxial rays only for image formation. The refractive index of the sphere is fraction numerator 3 over denominator 2 end fraction and that of the liquid is fraction numerator 4 over denominator 3 end fraction.

The value of h is (nearly equal to)

  1. 8 cm    
  2. 9 cm    
  3. 14 cm    
  4. 15 cm.    

The correct answer is: 15 cm.

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