A transparent sphere of radius R has a cavity of radius 
as shown in figure. Find the refractive index of the sphere if a parallel beam of light falling on left surface focuses at point P.
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Ans. 2
Sol. Let refractive index for glass is μ after first refraction image distance is v
= 
v = 
Now second refraction take place
u 1 = v – R
– R = 
and
image will formed at P i.e. at v 1 = R
– 
= 
μ 2 – 3 μ + 1 = 0
μ = 
= 2.61
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