Q. 42

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.

Answer :

Radius of the transparent sphere= r


Refraction at convex surface


According to question,


Object distance u= -




(a) At the surface of the sphere.


42a.PNG


Image distance = v=2r


Radius of curvature =(R) = r


By lens equation







(b) At the center of the sphere.


42b.PNG


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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