Question

What is meant by polarisation angle? Find angle between reflected and refracted rays whenever light rays incident on polarisation angle. Draw suitable ray diagram.

Answer 1

Polarisation angle is the angle at which unpolarized light or other electromagnetic radiation must be incident upon a nonmetallic surface for the reflected radiation to acquire maximum plane polarization — called also Brewster angle.

According to Brewstar's Law, at polarising angle, the reflected ray and refracted ray are mutually perpendicular.

So, the formular for Brewstar's Law is,

${}^1{n}_2=\tan i_p$, that is the tangent of polarising angle is equal to the refractive index of the reflecting medium w.r.t the surrounding.

we know, $\frac{\sin i_p}{\cos i_p}{=}^1{n}_2..........\left(i\right)$

By Snell's Law, $\frac{\sin i_p}{\sin r}{=}^1{n}_2...........\left(ii\right)$, r is the refraction angle.

equating equations(i) and (ii), we get

$\frac{\sin i_p}{\cos i_p}=\frac{\sin i_p}{\sin r}or,\cos i_p=\sin r..........\left(iii\right)$

From the figure, $i_p=r^{\prime }$ as incidence angle=reflecting angle.

Hence, equation(iii) can be written as,

$\cos r^{\prime }=\sin ror,\sin (90-r^{\prime })=\sin r$, as $cos\theta =\sin (90-\theta )$

$\Rightarrow 90-r^{\prime }=ror,r+r^{\prime }=90°...........\left(iv\right)$

From the figure, $r^{\prime }+\angle COB+r=180°$

$or,\angle COB=90°,\left(fromequation\right(iv\left)\right)$

Hence the angle between reflected ray and refracted ray is 90°