Question

A transparent cylinder has its right half polished so as to act as a mirror. A paraxial light ray is incident from left, that is parallel to principal axis, exits parallel to the incident ray as shown. The refractive index of the material of the cylinder is________.

Answer 1

For refraction formula at spherical surface, we use
$v=2 R ; u=\infty ; \mu_{1}=1 \text { and } \mu_{2}=\mu$
Using refraction formula, we have $\frac{\mu_{2}}{v}-\frac{\mu_{1}}{u}=\frac{\mu_{2}-\mu_{1}}{R}$
$\Rightarrow \frac{\mu}{2 R}-\frac{1}{\infty}=\frac{\mu-1}{R} $
$\Rightarrow \mu=2 \mu-2 \Rightarrow \mu=2$