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Q.

A spherical ball of transparent material has index of refraction μ . A narrow beam of light AB is aimed as shown. What must the index of refraction be in order that the light is focused at the point C on the opposite end of the diameter from where the light entered? Given that x << R.

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answer is 2.

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Detailed Solution

From the figure, we observe that BO = OC 

So, if OBC=BCO=r(say) and i be the angle of incidence, then

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i=r+r=2r
μ=sinisinrμ=sin2rsinr2rr=2

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