Question

In the given situation, a spherical transparent surface of radius $R$ is placed. The refractive index of sphere is such that image for an object kept at distance $R$ is formed at the same distance of the opposite side. What is refractive index of sphere?

• A. $1.5$
• B. $1.75$
• C. $1.25$
• D. $2$

Answer 1

The correct option is D $2$

From the symmetry of the figure, ray inside the sphere is parallel to principal axis. Taking refraction at $A$.

$\frac{{\mu }_2}{v}-\frac{{\mu }_1}{u}=\frac{{\mu }_2-{\mu }_1}{R}$

$\frac{\mu }{\infty }-\frac{1}{-R}=\frac{\mu -1}{R}$

$\frac{1}{R}=\frac{\mu -1}{R}⟹\mu -1=1$

$⟹\mu =2$