First slide

Ray optics

Question

The refracting angle of a prism, made of a transparent material is 120^o. A ray of light is incident on one refracting surface of the prism. What should be the maximum refracting index of the material of the prism for which the ray of light can pass into the surrounding air through the other refracting surface?

Moderate

A

$\sqrt{\frac{3}{2}}$
B

$\sqrt{3}$
C

$2 / \sqrt{3}$
D

$\sqrt{2}$

Solution

To get an emergent ray through the other refracting surface $A \leq 2 \sin^{- 1} (\frac{1}{μ})$
$∴ \sin^{- 1} \frac{1}{μ} ≥ \frac{A}{2} \Rightarrow μ \leq \frac{1}{\sin \frac{A}{2}}$
$∴ μ_{m a x} = \frac{1}{\sin \frac{A}{2}} = \frac{1}{\sin (\frac{120^{o}}{2})} = \frac{2}{\sqrt{3}}$

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