Question

Unpolarized light of intensity $I_0$ is incident on two polaroids placed coaxially. The transmission axis of the second polaroid is at an angle of $60^\circ$ to the first. The intensity of emerging light is:

• A. $I_0/2$
• B. $I_0/4$
• C. $I_0/8$
• D. $3I_0/8$

Hint:

First polaroid always reduces unpolarized intensity by exactly 50%. Then apply Malus's Law ($I = I_1\cos^2\theta$) for the second polaroid.

Answer 1

The Correct Option is C

Step 1: Concept
When unpolarized light passes through the first polaroid, its intensity is halved. When polarized light passes through a second polaroid, Malus's Law applies: $I = I_1\cos^2\theta$.

Step 2: Meaning
After the first polaroid: $I_1 = \dfrac{I_0}{2}$. The angle between the axes is $\theta = 60^\circ$.

Step 3: Analysis
\[I_2 = I_1\cos^2 60^\circ = \frac{I_0}{2}\times\left(\frac{1}{2}\right)^2 = \frac{I_0}{2}\times\frac{1}{4} = \frac{I_0}{8}.\]

Step 4: Conclusion
The intensity of the emerging light is $\dfrac{I_0}{8}$. Final Answer: (C)