Question

Two polaroids are inclined at an angle of \(30^\circ\). Unpolarized light of intensity \(40\,W\,m^{-2}\) is incident on the first polaroid. Find the intensity after emerging from the second polaroid.

• A. \(30\,W\,m^{-2}\)
• B. \(20\,W\,m^{-2}\)
• C. \(10\,W\,m^{-2}\)
• D. \(15\,W\,m^{-2}\)

Hint:

Remember: \[ I=\frac{I_0}{2}\cos^2\theta \] for unpolarized light passing through two polaroids.

Answer 1

The Correct Option is D

Concept: When unpolarized light passes through a polaroid, its intensity becomes half. \[ I_1=\frac{I_0}{2} \] When this polarized light passes through a second polaroid making an angle \(\theta\) with the first, Malus law is used: \[ I=I_1\cos^2\theta. \]

Step 1: Find intensity after first polaroid. Given, \[ I_0=40\,W\,m^{-2} \] Therefore, \[ I_1=\frac{40}{2} \] \[ I_1=20\,W\,m^{-2} \]

Step 2: Apply Malus law. Angle between polaroids, \[ \theta=30^\circ \] Thus, \[ I=20\cos^2 30^\circ \] \[ =20\left(\frac{\sqrt3}{2}\right)^2 \] \[ =20\left(\frac34\right) \] \[ =15\,W\,m^{-2} \]

Step 3: Final answer. \[ \boxed{15\,W\,m^{-2}} \] Hence, \[ \boxed{(D)} \]