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 be focuses

(a) At the surface of the sphere.

(b) At the center of the sphere.

Radius of the transparent sphere= r

Refraction at convex surface

According to question,

Object distance u= -

(a) At the surface of the sphere.

Image distance = v=2r

Radius of curvature =(R) = r

By lens equation

⇒

⇒

⇒

⇒

(b) At the center of the sphere.

Image distance v=r

Radius of curvature = r

By lens equation

⇒

⇒

⇒

The above equation is not possible. Hence, image is not possible to focus at center.

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