If 10% of intensity is passed from analyser, then, the angle by which analyser should be rotated such that transmitted intensity becomes zero. (Assume no absorption by analyser and polarizer).

Options

A. ` 90 ^(@) `
B. ` 71.6 ^(@) `
C. ` 18.4 ^(@) `
D. ` 45^(@)`

Answer

To solve the problem, we will use Malus's Law, which states that the intensity of polarized light passing through a polarizer (analyzer) is given by:

\[ I = I_0 \cos^2(\theta) \]

where:
- \( I \) is the transmitted intensity,
- \( I_0 \) is the initial intensity,
- \( \theta \) is the angle between the light's polarization direction and the axis of the polarizer.

### Step-by-Step Solution:

1. **Understanding the Given Information:**
- We know that 10% of the intensity is passed through the analyzer. This means:
\[ I = 0.1 I_0 \]

2. **Applying Malus's Law:**
- According to Malus's Law:
\[ I = I_0 \cos^2(\theta) \]
- Substituting the value of \( I \):
\[ 0.1 I_0 = I_0 \cos^2(\theta) \]

3. **Canceling \( I_0 \):**
- Since \( I_0 \) is not zero, we can divide both sides by \( I_0 \):
\[ 0.1 = \cos^2(\theta) \]

4. **Finding \( \theta \):**
- Taking the square root of both sides:
\[ \cos(\theta) = \sqrt{0.1} \]
- Therefore:
\[ \theta = \cos^{-1}(\sqrt{0.1}) \]

5. **Calculating \( \theta \):**
- Using a calculator, we find:
\[ \theta \approx 71.6^\circ \]

6. **Finding the Angle to Rotate the Analyzer:**
- To find the angle by which the analyzer should be rotated to make the transmitted intensity zero, we need to rotate it to 90 degrees from the current angle:
\[ \text{Angle to rotate} = 90^\circ - \theta \]
- Substituting the value of \( \theta \):
\[ \text{Angle to rotate} = 90^\circ - 71.6^\circ \]
\[ \text{Angle to rotate} = 18.4^\circ \]

### Final Answer:
The analyzer should be rotated by **18.4 degrees** to make the transmitted intensity zero.