Question

A triangular prism of glass is shown in figure. A ray incident normally on one face is totally reflected. If $\theta$ is ${45}^{\circ }$, the index of refraction of glass is

• A. Less than $\sqrt{2}$
• B. Equal to $\sqrt{2}$
• C. Greater than $\sqrt{2}$
• D. None of the above

Answer 1

The correct option is C Greater than $\sqrt{2}$

As TIR happens here,
${\theta }_C<\theta$
Applying sin on both sides of inequality
$\sin {\theta }_C<\sin \theta$
We know that
${\theta }_C={\sin }^{-1}\left(\frac{1}{\mu }\right)$
$\mu =\left(\frac{1}{\sin {\theta }_C}\right)$

$\Rightarrow \frac{1}{\mu }<\frac{1}{\sqrt{2}}\Rightarrow \mu >\sqrt{2}$.