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

Using refraction formula $\frac{{ }_1{\mu }_2-1}{R}=\frac{{ }_1{\mu }_2}{v}-\frac{1}{u},$

 in given case, medium (1) is glass and (2) is air .So $\frac{g{\mu }_a-1}{R}=\frac{g{\mu }_a}{v}-\frac{1}{u}\Rightarrow \frac{\frac{1}{1.5}-1}{-6}=\frac{1}{1.5v}-\frac{1}{-6}\Rightarrow \frac{1-1.5}{-6}=\frac{1}{v}+\frac{1.5}{6}\Rightarrow \frac{0.5}{6}=\frac{1}{v}+\frac{1}{4}$

$\Rightarrow \frac{1}{v}=\frac{1}{12}-\frac{1}{4}=-\frac{2}{12}=-\frac{1}{6}\Rightarrow v=6\mathrm{cm}$