The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5^ from the polarization axi…

Question

The intensity of transmitted light when a polaroid sheet, placed between two crossed polaroids at 22.5^ from the polarization axis of one of the polaroids, is (I0 is the intensity of polarised light after passing through the first polaroid):

1. A. I0/2
2. B. I0/4
3. C. I0/8 (Correct answer)
4. D. I0/16

Correct Answer

Option C — I0/8

Detailed Solution & Explanation

The correct answer is $\dfrac{I_0}{8}$.

Key Points

• After the middle polaroid (at $22.5^\circ$): $I_1=I_0\cos^2(22.5^\circ)$.
• The last polaroid is crossed with the first, so it is at $90^\circ-22.5^\circ$ from the middle one: $I_2=I_1\cos^2(90^\circ-22.5^\circ)=I_0\cos^2(22.5^\circ)\sin^2(22.5^\circ)$.
• Using $2\sin\theta\cos\theta=\sin2\theta$: $I_2=\dfrac{I_0}{4}\sin^2(45^\circ)=\dfrac{I_0}{4}\cdot\dfrac{1}{2}=\dfrac{I_0}{8}$.