Question

A ray of light incident normally on the horizontal face of the slab and just fail to emerge from the diagonal face of the prism. If prism angle is ${30}^o$ then refractive index of the prism can be

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. slightly greater than 2
• D. slightly less than 2

Answer 1

Answer: (C)

slightly greater than 2

For the ray to graze on the face AC, i-e, $e={90}^o$

From geometry, ${\theta }_c={30}^o$

Let the refractive index of the prism be $\mu$.

Snell' law, ${\mu }_o\times sin{30}^o=1\times 1$

$⟹{\mu }_o=2$

For total internal to occur, means $\theta >{\theta }_c$

$⟹{\mu }_o<2$