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An opaque sphere of radius a is just immersed in a transparent liquid as shown in figure. A point source is placed on the vertical diameter of the sphere at a distance a/2 from the top of the sphere. One ray originating from the point source after refraction from the air liquid interface forms tangent to the sphere. The angle of refraction for that particular ray is 30°. The refractive index of the liquid is

  1. fraction numerator 2 over denominator square root of 3 end fraction    
  2. fraction numerator 3 over denominator square root of 5 end fraction    
  3. fraction numerator 4 over denominator square root of 5 end fraction    
  4. fraction numerator 4 over denominator square root of 7 end fraction    

The correct answer is: fraction numerator 4 over denominator square root of 7 end fraction

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