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Q.

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

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answer is 2.

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Detailed Solution

For refraction at surface, we use
$v = 2 R, u = \infty, μ_{1} = 1 a n d μ_{2} = μ$
Using refraction formula, we have
$\frac{μ_{2}}{v} - \frac{μ_{2}}{v} = \frac{μ_{2} - μ_{1}}{R} \Rightarrow \frac{μ_{2}}{2 R} + \frac{μ_{1}}{\infty} = \frac{μ_{2} - μ_{1}}{R}$

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