A polarizer - analyser set is adjusted such that the intensity of llight coming out of the analyser is just `36%` of the original intensity. Assuming that the polarizer - analyser set does not absorb any light, the angle by which the analyser needs to be rotated further, to reduce the output intensity to zero, is `(sin^(-1)((3)/(5))=37^(@))`

Options

A. `53^(@)`
B. `37^(@)`
C. `90^(@)`
D. `45^(@)`

Answer

To solve the problem, we need to determine the angle by which the analyser must be rotated further to reduce the output intensity to zero, given that the intensity of light coming out of the analyser is currently 36% of the original intensity.

### Step-by-Step Solution:

1. **Understanding the Problem**:
We know that the intensity \( I \) of light after passing through the polarizer-analyser set is given as 36% of the original intensity \( I_0 \). This can be expressed mathematically as:
\[ I = 0.36 I_0 \]

2. **Using Malus's Law**:
According to Malus's Law, the intensity of light passing through a polarizer-analyser set is given by:
\[ I = I_0 \cos^2 \theta \]
where \( \theta \) is the angle between the light's polarization direction and the axis of the analyser.

3. **Setting Up the Equation**:
From the above equation, we can set up the following equation:
\[ 0.36 I_0 = I_0 \cos^2 \theta \]
Dividing both sides by \( I_0 \) (assuming \( I_0 \neq 0 \)):
\[ 0.36 = \cos^2 \theta \]

4. **Finding \( \cos \theta \)**:
Taking the square root of both sides:
\[ \cos \theta = \sqrt{0.36} = 0.6 \]
This can also be expressed as:
\[ \cos \theta = \frac{3}{5} \]

5. **Calculating \( \theta \)**:
To find the angle \( \theta \):
\[ \theta = \cos^{-1}\left(\frac{3}{5}\right) \]
Using a calculator or trigonometric tables, we find:
\[ \theta \approx 53^\circ \]

6. **Finding the Required Rotation**:
The analyser needs to be rotated further to reduce the intensity to zero. The maximum angle for the analyser is \( 90^\circ \). Therefore, the angle by which the analyser needs to be rotated further is:
\[ \text{Rotation} = 90^\circ - \theta = 90^\circ - 53^\circ = 37^\circ \]

### Final Answer:
The angle by which the analyser needs to be rotated further to reduce the output intensity to zero is \( 37^\circ \).

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