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Q.

An object O is stuck on the surface of a transparent solid sphere of radius 20 cm. Find refractive index of the sphere such that rays from the object after refraction from the opposite side emerge as a parallel beam, as shown. Also prove that refractive index has the same value, in the given situation, for any value of radius of sphere.

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a

2.0

b

1.0

c

4.0

d

3.0

answer is B.

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Detailed Solution

Refraction at (1)

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μ1=μ,μ2=1,u=2R,v=,R=R

μ2vμ1u=μ2μ1R

1μ2R=1μR

μ2R=μ1R

μ=2μ2

μ=2.0

Refractive index is μ=2, for any value of R.

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