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Question

A point object is placed at the center of a glass sphere of radius 6 cm and refractive index 1.5. find the distance of the virtual image from the surface of the sphere.

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Solution

Considering refraction from the left surface, and using refraction formula,
μ2vμ1u=μ2μ1+R

Since object is at center of the sphere, object distance,
u=+R

Substituting, we get,
μ2vμ1R=μ2Rμ1R
μ2v=μ2R
v=R

This means the image is also formed at the center. This happens because light rays does not bend at the spherical surface, as all rays are passing through the center.

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