Question

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

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

Answer 1

Answer: (C)

According to Malus law, we have
$I=I_{0} \cos ^{2} \theta \Rightarrow \frac{I}{I_{0}}=\cos ^{2} \theta$
Since the observed intensities are same for all values of $\theta$,
therefore, for the angles given in options, the observed intensity
should be same as well for all $\theta, \theta=8^{\circ}, 38^{\circ}, 188^{\circ}$ and $218^{\circ}, \frac{I}{I_{0}} \sim 0.9 $
and for $\theta=203^{\circ}, \frac{I}{I} \sim 0.9 .$
Therefore, angle between direction of polarisation and $x$ axis is $203^{\circ} .$