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Easy

Question

A point source of light S is placed at the bottom of a vessel containing a liquid of refractive index 5/3. A person is viewing the source from above the surface. There is an opaque disc D of radius 1 cm floating on the surface of the liquid. The centre of the disc lies vertically above the source S. The liquid from the vessel is gradually drained out through a tap. The maximum height of the liquid for which the source cannot be seen at all from above is

  1. 1.50 cm    
  2. 1.64 cm    
  3. 1.33 cm    
  4. 1.86 cm    

The correct answer is: 1.33 cm


    Suppose the maximum height of the liquid is h for which the source is not visible.
    Hence radius of the disc

    r equals fraction numerator h over denominator square root of mu to the power of 2 end exponent minus 1 end root end fraction
    1 equals fraction numerator h over denominator square root of open parentheses fraction numerator 5 over denominator 3 end fraction close parentheses to the power of 2 end exponent minus 1 end root end fraction rightwards double arrow h equals 1.33 c m

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