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.

Answer 1

Considering refraction from the left surface, and using refraction formula,
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{+R}$

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

Substituting, we get,
$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{R}=\frac{{\mu }_2}{R}-\frac{{\mu }_1}{R}$
$\frac{{\mu }_2}{v}=\frac{{\mu }_2}{R}$
$v=R$

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.