A light ray is incident on a transparent medium of $\mu =1.732$ at the polarizing angle. The angle of refraction is :
A. ${{60}^{o}}$
B. ${{30}^{o}}$
C. ${{45}^{o}}$
D. ${{90}^{o}}$

Hint: The concept involved is of polarizing angle which is also known as brewster's angle and also the basic law of refraction which is snells’ law.
Brewster's angle (also known as the polarization angle) is an angle of incidence at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface, with no reflection. When unpolarized light is incident at this angle, the light that is reflected from the surface is therefore perfectly polarized.
Snell's law states that product of sine of incident and refracted ray product with refractive indices of the medium are equal.

Complete step-by-step answer:
In our case the incident angle is polarizing angle or brewster angle.it is the angle at which incident non-polarized light when reflected and refracted the reflected component is completely polarized.

The polarizing angle $\theta $ in terms of the refractive index $\mu $ on which the ray is striking is
$\tan \theta =\mu $
Given value of $\mu $ is= 1.732
The incident angle at which ray strikes is
$\Rightarrow \tan \theta =1.732$
$\theta ={{\tan }^{-1}}\left( 1.732 \right)$
$\Rightarrow \theta ={{60}^{o}}$
Now we will apply snells’ law at the surface assuming air to be the first medium
$\sin \theta \times {{n}_{1}}=\sin r\times {{n}_{_{2}}}$
We have to find refracting angle $r$
${{n}_{1}}=1$
${{n}_{2}}=1.732$
$\theta ={{60}^{o}}$
Putting the values,
$\Rightarrow \dfrac{\sin {{60}^{o}}\times 1}{1.732}=\sin r$
$\Rightarrow r={{\sin }^{-1}}\left( \dfrac{1.732}{2\times 1.732} \right)$ We know that,${{\sin }^{-1}}\left( \dfrac{1}{2} \right)={{30}^{o}}$
$\Rightarrow r={{30}^{o}}$
So the refracting angle has come and the correct option is B

So, the correct answer is “Option B”.

Note: There are many applications of polarizing angle.
Polarized sunglasses use the principle of Brewster's angle to reduce glare from the sun reflecting off horizontal surfaces such as water or road.
Polarizing sunglasses use a polarizing material such as Polaroid sheets to block horizontally-polarized light, preferentially blocking reflections from horizontal surfaces.