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 can follow these steps:

### Step 1: Understand the relationship between intensity and angle
According to Malus's Law, the intensity of light passing through a polarizer-analyzer set is given by:
\[ I = I_0 \cos^2(\theta) \]
where \( I_0 \) is the initial intensity, \( I \) is the transmitted intensity, and \( \theta \) is the angle between the polarizer and the analyzer.

### Step 2: Set up the equation with the given information
We know that the intensity coming out of the analyzer is 36% of the original intensity:
\[ I = 0.36 I_0 \]
Substituting this into Malus's Law gives:
\[ 0.36 I_0 = I_0 \cos^2(\theta) \]

### Step 3: Simplify the equation
Dividing both sides by \( I_0 \) (assuming \( I_0 \neq 0 \)):
\[ 0.36 = \cos^2(\theta) \]

### Step 4: Solve for \( \cos(\theta) \)
Taking the square root of both sides:
\[ \cos(\theta) = \sqrt{0.36} = \frac{6}{10} = \frac{3}{5} \]

### Step 5: Find the angle \( \theta \)
To find \( \theta \), we take the inverse cosine:
\[ \theta = \cos^{-1}\left(\frac{3}{5}\right) \]
Calculating this gives:
\[ \theta \approx 53^\circ \]

### Step 6: Determine the final angle for zero intensity
To reduce the intensity to zero, the angle between the polarizer and analyzer must be \( 90^\circ \).

### Step 7: Calculate the additional rotation needed
The additional rotation required to achieve this is:
\[ \text{Additional rotation} = 90^\circ - \theta \]
Substituting the value of \( \theta \):
\[ \text{Additional rotation} = 90^\circ - 53^\circ = 37^\circ \]

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

---