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Q. 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

KEAMKEAM 2015Wave Optics

Solution:

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,
$d=i-r=60^{\circ}-30^{\circ}=30^{\circ}$