Question

(a) Define wave-front. Use Huygen's principle to verify the laws of refraction.
(b) How is linearly polarised light obtained by the process of scattering of light? Find the Brewster angle for air- glass interface, when the refractive index of glass $=1.5$.

Answer 1

A) A wavefront is a surface over which an optical wave has a constant.

B) Let AP be the wavefront of the incident wave, of speed in the first medium be $v_1$ and in the second medium be $v_2$ propagating in the direction $A{A}^{\prime }$ incident on the interface at an angle as shown in fig.

let $t$ be time to travel the wave $P$ to $P^{\prime }$, in the same time wavefront $A$ will reach at $A^{\prime }$,

So,

As per the diagram, $Sini=\frac{P{P}^{\prime }}{A{P}^{\prime }}$

$\therefore A{P}^{\prime }=P{P}^{\prime }Sini..................\left(1\right)$

Similarly $A{P}^{\prime }=A{A}^{\prime }Sinr.............\left(2\right)$ and, $P{P}^{\prime }=v_1\times t$ similarly $A{A}^{\prime }=v_2\times t$

Now from equation $\left(1\right)$ and $\left(2\right)$

$v_1\times tSini=v_2\times tSinr$

So $\frac{Sini}{Sin}=\frac{v_2}{v_1}$

We know that,

$n_1=\frac{c}{v_1}and{n}_2=\frac{c}{v_2}$

So $\frac{Sini}{Sinr}=\frac{n_2}{n_1}$ ,

This is the snell's rule for refraction.

B) When unpolarized light hits a reflective surface, the vertically polarised aspects are refracted into the surface.The horizontally polarised aspects are reflected off the surface and the light is now perceived as partially polarised.

When light is reflected, there is an angle at which this light is completely polarised. This is called Brewster's angle, after the Scottish physicist who discovered the law.

As per Brewster's rule$\mu =tan{i}_b$,

$1.5=tan{i}_b$

$\therefore i_b=ta{n}^{-1}\left(\frac{3}{2}\right)$