Question

A ray is incident on a prism of $\mu =\sqrt{2}$. Find the length of the optical path covered by ray inside the prism.

• A. $\sqrt{\frac{400}{3}}$
• B. $\sqrt{\frac{512}{3}}$
• C. $\sqrt{\frac{256}{3}}$
• D. $\sqrt{\frac{441}{3}}$

Answer 1

The correct option is B $\sqrt{\frac{512}{3}}$


Using Snell's law,
$1\sin {45}^{\circ }=\sqrt{2}\sin \theta$
$\frac{1}{\sqrt{2}}=\sqrt{2}\sin \theta$
$\sin \theta =\frac{1}{2}$
$\theta ={30}^{\circ }$


$\frac{\frac{X}{2}}{8}=\tan {30}^{\circ }$

$\frac{X}{16}=\tan {30}^{\circ }=\frac{1}{\sqrt{3}}$
$X=\frac{16}{\sqrt{3}}$

Optical path $=n$ (Geometrical path)
$=\sqrt{2}\times \frac{16}{\sqrt{3}}=\sqrt{\frac{2\times 256}{3}}=\sqrt{\frac{512}{3}}$