Question

A plane polarized light is incident on a polarizer with its pass axis making angle $\theta$ with the x-axis, as shown in the figure. At four different values of $\theta ,\theta =8^{\circ },{38}^{\circ },{188}^{\circ }$ and ${218}^{\circ }$ the observed internists are same. What is the angular between the direction of polarization and the x-axis?

• A. ${98}^o$
• B. ${128}^o$
• C. ${203}^o$
• D. ${45}^o$

Answer 1

The correct option is C ${203}^o$

The final intensity of polarized light

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

$\mathrm{fos}\theta =8^{\circ }$

Intensity $=\frac{I_0}{2}{\cos }^2(8-\alpha )$

$\theta ={38}^{\circ }$

$I_2=\frac{I_0}{2}{\cos }^2(38-\alpha )$

$\theta ={188}^{\circ }$

$I_3=\frac{I_0}{2}{\cos }^2(188-\alpha )$

$\theta ={218}^{\circ }$

$I_4=\frac{I_0}{2}{\cos }^2(218-\alpha )$

Given $I_1=I_2=I_3=I_4$

this happens when $\alpha ={203}^{\circ }$

$I_1=I_2=I_3=I_4=\frac{I_0}{2}{\cos }^2\left(15\right)$

$\alpha ={203}^{\circ }$

option C is Correct.