A polaroid sheet $P_2$ is rotated by an angle θ (angle between pass axies of $P_1$ and $P_2$) between two crossed polaroids $P_1$ and $P_3$. The intensity of transmitted light will be maximum for:

$θ=45°$

The correct answer is Option (3) → $θ=45°$

The intensity of transmitted light through two polaroids is governed by Maul's law.

$I=I_0\cos^2(θ)$

where,

$I_0$ = Intensity of light incident on polarizer.

θ = Angle between light's polarization direction and axis of polarizer.

Given,

• $P_1,P_2,P_3$ are 3 polaroids.
• pass axis of $P_1$ is aligned in a particular direction and the pass axis of $P_2$ is rotated by an angle θ relative to $P_1$.
• pass axis of $P_3$ is perpendicular to $P_1$

for maximum intensity to be transmitted through $P_3$ the angle between the pass axiz of $P_2$ and $P_3$ must be zero. Since $P_1$ and $P_3$ are crossed (90° to each other).

The condition will be satisfied when the angle between $P_1$ and $P_2$ is 45°.