1. Show using a proper diagram how unpolarised light can be linea… - Vidyadip

Question

Show using a proper diagram how unpolarised light can be linearly polarised by reflection from a transparent glass surface.
The figure shows a ray of light falling normally on the face $AB$ of an equilateral glass prism having refractive index $\frac{3}{2},$ placed in water of refractive index $\frac{4}{3}.$ Will this ray suffer total internal reflection on striking the face $AC$? Justify your answer.

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Answer

When unpolarised light ray is incident at an angle such that the angle between reflected of refracted rays is $90^\circ ,$ then reflected ray is linearly polarised. In that case incident angle is called polarising angle or Brewster angle $(i_P$ or $i_B)$.

For Total internal reflection $\Big(\frac{1}{\sin\text{i}_{\text{c}}}=\mu_{\text{DR}}\Big)$

$\sin\text{i}_{\text{c}}=\Big(\frac{1}{\sin\text{i}_{\text{c}}}=\mu_{\text{DR}}\Big)$
$\sin\text{i}_{\text{c}}=\mu_{\text{wg}}$
$\sin\text{i}_{\text{c}}=\frac{4}{3}\div\frac{3}{2}$
$=\frac{4}{3}\times\frac{2}{3}$
$\sin\text{i}_{\text{c}}=\frac{8}{9}=0.88$
Now, in this case
$\sin\text{i}=\sin60^\circ=\frac{\sqrt{3}}{2}=0.867$
$\because\ \sin\text{i}<\sin\text{i}_{\text{c}}$
$\text{So,}\ \text{i}<\text{i}_{\text{c}}$
So, ray will not suffer Total internal reflection.

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