Question

A beam of light $AO$ is incident on a glass slab $(\mu =1.732)$ in the direction shown. The reflected ray $OB$ is passed through a Nicol prism. On viewing through a Nicol prism, we can find on rotating the prism that

• A. the intensity is reduced down to zero and remains zero.
• B. the intensity reduces down somewhat and rises again.
• C. there is no change in intensity.
• D. the intensity gradually reduces to zero and then again increases.

Answer 1

The correct option is D the intensity gradually reduces to zero and then again increases.


According to Brewster's law

$\mu =\tan i_p$

$\Rightarrow i_p={\tan }^{-1}\left(1.732\right)={\tan }^{-1}\left(\sqrt{3}\right)={60}^{\circ }$

From the figure, $i={60}^{\circ }$

As, $i=i_P$

$\therefore$ Brewster's law is satisfied, so the reflected ray $OB$ will be plane polarized.

We know when a plane polarized light is passed through a Nicol prism $\left(\text{polaroid}\right)$, the intensity of emergent light varies as

$I=I_0{\cos }^2\theta$

$\therefore$ On rotating Nicol prism, $\theta$ varies,

When $\theta ={90}^{\circ }$, $I=0$ and
when $\theta =0^{\circ }$, $I=I_0$.

So, the intensity of the emergent ray gradually reduces to zero and then again increases.

So option $\left(D\right)$ is correct.

Why this Question? Concept : Condition of application of Brewster's law and variation of intensity of plane polarized light with angle between the transmission axis of polarizer and analyser.