Question

A system of three polarizers $P_1, P_2, P_3$ is set up such that the pass axis of $P_3$ is crossed with respect to that of $P_1$. The pass axis of $P_2$ is inclined at 60º to the pass axis of $P_3$. When a beam of unpolarized light of intensity $I_0$ is incident on $p_1$, the intensity of light transmitted by the three polarizers is $I$. The ratio $(I_0/I)$ equals (nearly) :

• A. 16.00
• B. 1.80
• C. 5.33
• D. 10.67

Answer 1

Answer: (D)

Since unpolarised light falls on $P_1 \, \Rightarrow $ intensity
of light transmitted from $P_1 = \frac{I_0}{2}$
Pass axis of $P_2$ will be at an angle of $30^\circ$ with
$P_1$
$\therefore $ Intensity of light transmitted from
$P_2 = \frac{I_0}{2} \, cos^2 \, 30^{\circ} = \frac{3I_0}{8}$
Pass axis of $P_3$ is at an angle of $60^\circ$ with $P_2$
$\therefore $ Intensity of light transmitted from
$ \, P_3 \, \frac{3I_0}{8} \, \, cos^2 60^{\circ} \, = \frac{3I_0}{32}$
$\therefore \, \, \bigg(\frac{I_0}{I}\bigg) \, = \, \frac{32}{3} \, \, = 10.67$