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An opaque sphere of radius a is just imm...

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 all 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:

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