Question

Three identical polaroids \(P_1, P_2\) and \(P_3\) are placed one after another. The pass axis of \(P_2\) and \(P_3\) are inclined at an angle of \(60^\circ\) and \(90^\circ\) with respect to axis of \(P_1\). The source has an intensity \(256 \text{ W/m}^2\). The intensity of light at point ‘O’ is

• A. \(24 \text{ W/m}^2\)
• B. \(20 \text{ W/m}^2\)
• C. \(16 \text{ W/m}^2\)
• D. \(8 \text{ W/m}^2\)

Hint:

Apply Malus's law at each polaroid, remembering that unpolarised light loses half its intensity at the first polaroid.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept
Unpolarised light passing the first polaroid has its intensity halved.
Afterwards, Malus's law applies: \(I=I_0\cos^2\theta\).

Step 2: After P1
\(I_1=\dfrac{256}{2}=128\ \text{W/m}^2\)

Step 3: After P2 and P3
P2 is at \(60^{\circ}\) to P1: \(I_2=128\cos^2 60^{\circ}=128\times\dfrac{1}{4}=32\ \text{W/m}^2\)
P3 is at \(90^{\circ}\) to P1, so \(30^{\circ}\) to P2: \(I_3=32\cos^2 30^{\circ}=32\times\dfrac{3}{4}=24\ \text{W/m}^2\)

Step 4: Compare the options
The intensity at O is \(24\ \text{W/m}^2\), the first option.

Final Answer:
The final intensity at O is 24 W/m\(^2\). \[ \boxed{\text{(A) }24\ \text{W/m}^2} \]