A narrow pencil of parallel light is incident normally on a- solid transparent sphere of radius r. What should be the refractive index if the pencil is to he focused (a) at the surface of the sphere, (b) at the centre of the sphere.

A narrow pencil of parallel light is incident normally on a- solid tra

1.	A narrow pencil of parallel light is incident normally on a- solid transparent sphere of radius r. What should be the refractive index if the pencil is to he focused (a) at the surface of the sphere, (b) at the centre of the sphere.
Answer» We should CONSIDER TWO cases:For refraction at first surface A:U= -∞μ1=1μ2=?A) when focused on surface V=2rR=rμ2/V- μ1/u= μ2-μ1/Rμ2/2r = μ2-1/rμ2= 2μ2-2μ2= 2B) When focused at centre u= r1R=rμ2/V - μ1/u= μ2-μ1/Rμ2/R = μ2-1/rμ2= μ2-1Which is not possiblehence it cannot FOCUS at centre

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A narrow pencil of parallel light is incident normally on a- solid transparent sphere of radius r. What should be the refractive index if the pencil is to he focused (a) at the surface of the sphere, (b) at the centre of the sphere.

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