Question

If a ray of light is incident at a glass surface at the Brewster's angle of ${60}^{\circ }$, then the angle of deviation inside glass is

• A. ${90}^{\circ }$
• B. ${60}^{\circ }$
• C. ${45}^{\circ }$
• D. ${30}^{\circ }$
• E. ${15}^{\circ }$

Answer 1

The correct option is D ${30}^{\circ }$

Key Concept According to Brewster law, when a beam of unpolarised light is reflected from a transparent medium, the reflected light is completely plane polarised at a certain of incidence, called angle of polarisation.
Given, Brewster's angle, $\theta ={60}^{\circ }$
We know that, $\mu =\tan \theta ...\left(i\right)$
$\Rightarrow \mu =\tan {60}^{\circ }=\sqrt{3}$
Now, $\mu =\frac{\sin i}{\sin r}$
$\Rightarrow \sin r=\frac{\sin r}{\mu }=\frac{\sin {60}^{\circ }}{\sqrt{3}}\Rightarrow \frac{\sqrt{3}/2}{\sqrt{3}}$
$\Rightarrow \sin r=\frac{1}{2}\Rightarrow r={\sin }^{-1}\left(\frac{1}{2}\right)={30}^{\circ }$.
Angle of deviation inside the glass,
$d=i-r={60}^{\circ }-{30}^{\circ }={30}^{\circ }$.