A polarizer-analyser set is a adjusted such that the intensity of light coming out of the analyser is just 12.5 % of the original intersity. Assuming that the polarizer – analyser set does not absorb any light the angle by which the analyser need to be rotated further to reduce the output intensity to be zero, is :

Options

A. `45^(@)`
B. `90^(@)`
C. `60^(@)`
D. `30^(@)`

Explanation

To solve the problem, we need to use Malus's Law, which states that the intensity of light passing through a polarizer-analyzer setup is given by:

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

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

### Step-by-Step Solution:

1. **Identify the Given Information**:
- The intensity of light coming out of the analyzer is 12.5% of the original intensity.
- This can be expressed as:
\[ I = 0.125 I_0 \]

2. **Apply Malus's Law**:
- According to Malus's Law, after passing through the polarizer and analyzer, we can express the transmitted intensity as:
\[ I = I_0 \cos^2(\theta) \]
- Here, \( \theta \) is the angle between the polarizer and analyzer.

3. **Set Up the Equation**:
- From the information given:
\[ 0.125 I_0 = I_0 \cos^2(\theta) \]
- We can cancel \( I_0 \) from both sides (assuming \( I_0 \neq 0 \)):
\[ 0.125 = \cos^2(\theta) \]

4. **Solve for \( \theta \)**:
- Taking the square root of both sides:
\[ \cos(\theta) = \sqrt{0.125} = \frac{1}{2\sqrt{2}} \]
- This simplifies to:
\[ \cos(\theta) = \frac{1}{4} \]
- Now, we find \( \theta \):
\[ \theta = \cos^{-1}\left(\frac{1}{2}\right) \]
- This gives:
\[ \theta = 60^\circ \]

5. **Determine the Angle for Zero Intensity**:
- To reduce the output intensity to zero, the angle between the polarizer and analyzer must be \( 90^\circ \).
- Therefore, we need to find how much further the analyzer needs to be rotated:
\[ \text{Angle to rotate} = 90^\circ - 60^\circ = 30^\circ \]

### Final Answer:
The angle by which the analyzer needs to be rotated further to reduce the output intensity to zero is **30 degrees**.

---