Question

The angle of polarisation of a medium is $60°$. What will be critical angle for this?

• A. ${\sin }^{-1}\left(\sqrt{3}\right)$
• B. ${\tan }^{-1}\left(\sqrt{3}\right)$
• C. ${\cos }^{-1}\left(\sqrt{3}\right)$
• D. ${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Answer 1

The correct option is D

${\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)$

Step 1: Given data

The angle of polarisation of a medium ${\theta }_p=60°$

Step 2: Calculate refractive index

Given, angle of polarisation, ${\theta }_p=60°$

We know that,

$\mu =\tan \left({\theta }_p\right)$

where $\mu$ is the refractive index.

Thus,

$\begin{array}{rcl}\mu & =& \tan \left(60°\right)\\ \therefore \mu & =& \sqrt{3}\end{array}$

Step 3: Calculate critical angle

We also know that,

$\mu ·\sin \left(C\right)=1$

where $C$ is the critical angle.

Thus,

$\begin{array}{rcl}\sin \left(C\right)& =& \frac{1}{\mu }\\ C& =& {\sin }^{-1}\left(\frac{1}{\mu }\right)\\ \therefore C& =& {\sin }^{-1}\left(\frac{1}{\sqrt{3}}\right)\end{array}$

Hence, option D is correct.