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

Answer: (D)

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, $\mu =\tan \theta$ ...(i)
$\Rightarrow \mu =\tan 60^{\circ }=\sqrt{3}$
Now, $\mu =\frac{\sin i}{\sin r}$
$\Rightarrow \sin r=\frac{\sin i}{\mu }=\frac{\sin 60^{\circ }}{\sqrt{3}}\Rightarrow \frac{\sqrt{3}/2}{\sqrt{3}}$
$\Rightarrow \sin r=\frac{1}{2}$
$\Rightarrow r={\sin }^{-1}\left(\frac{1}{2}\right)=30^{\circ }$
Angle of deviation inside the glass,
$d=i-r=60^{\circ }-30^{\circ }=30^{\circ }$