Wave Optics - Result Question 25

27. Two Polaroids $P_1$ and $P_2$ are placed with their axis perpendicular to each other. Unpolarised light $I_0$ is incident on $P_1$. A third polaroid $P_3$ is kept in between $P_1$ and $P_2$ such that its axis makes an angle $45^{\circ}$ with that of $P_1$. The intensity of transmitted light through $P_2$ is

[2017]

(a) $\frac{I_0}{4}$

(b) $\frac{I_0}{8}$

(c) $\frac{I_0}{16}$

(d) $\frac{I_0}{2}$

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Answer:

Correct Answer: 27. (b)

Solution:

(b)

According to Malus law, $I=I_0 \cos ^{2} \theta$

$I_1=\frac{I_0}{2}$

$I_2=\frac{I_0}{2} \cos ^{2} 45^{\circ}=\frac{I_0}{2} \times \frac{1}{2}=\frac{I_0}{4}$

$I_3=\frac{I_0}{4} \cos ^{2} 45^{\circ}=\frac{I_0}{8}$