Question

The angle between the axes of the polarizer and the analyzer is $60^{\circ}$. The ratio of the intensity of unpolarized light incident on the polarizer and the intensity of the polarized light emerging from the analyzer is

• A. 1:1
• B. 8:1
• C. 4:1
• D. 2:1

Hint:

Remember: Unpolarized light intensity halves upon passing through an ideal polarizer ($I \to I/2$). Subsequent polarized light follows $I' = I \cos^2 \theta$.

Answer 1

The Correct Option is B

Step 1: Malus' Law and Polarization:
Let the intensity of incident unpolarized light be $I_0$. When unpolarized light passes through the first polarizer, its intensity becomes $I_1 = \frac{I_0}{2}$.
Step 2: Passing through Analyzer:
The light then passes through the analyzer oriented at an angle $\theta = 60^{\circ}$. According to Malus' Law, the emerging intensity $I_2$ is: \[ I_2 = I_1 \cos^2 \theta \] \[ I_2 = \left( \frac{I_0}{2} \right) \cos^2(60^{\circ}) \] \[ I_2 = \frac{I_0}{2} \left( \frac{1}{2} \right)^2 = \frac{I_0}{2} \times \frac{1}{4} = \frac{I_0}{8} \]
Step 3: Calculating Ratio:
We need the ratio of incident unpolarized intensity ($I_0$) to emerging intensity ($I_2$). \[ \text{Ratio} = \frac{I_0}{I_2} = \frac{I_0}{I_0 / 8} = 8:1 \]
Step 4: Final Answer:
The ratio is 8:1.