A plane polarized light is incident normally on a tourmaline plate. Its E vector make an angle of `60^(@)` with the optic axis of the plate. Find the percentage difference between initial and final intensities

Options

A. `50%`
B. `25%`
C. `75%`
D. `90%`

Explanation

To solve the problem of finding the percentage difference between the initial and final intensities of plane polarized light incident on a tourmaline plate, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have plane polarized light incident normally on a tourmaline plate. The electric field vector (E vector) makes an angle of \(60^\circ\) with the optic axis of the plate. We need to find the percentage difference between the initial intensity \(I\) and the final intensity \(I'\) after passing through the plate.

2. **Applying Malus's Law**:
According to Malus's Law, the intensity of polarized light after passing through a polarizer (in this case, the tourmaline plate) is given by:
\[ I' = I \cos^2 \theta \]
where \(I\) is the initial intensity, \(I'\) is the final intensity, and \(\theta\) is the angle between the light's electric field vector and the optic axis of the polarizer.

3. **Substituting the Given Values**:
Here, \(\theta = 60^\circ\). Therefore, we can calculate \(I'\):
\[ I' = I \cos^2(60^\circ) \]
We know that \(\cos(60^\circ) = \frac{1}{2}\), so:
\[ I' = I \left(\frac{1}{2}\right)^2 = I \cdot \frac{1}{4} \]

4. **Calculating the Final Intensity**:
Thus, the final intensity \(I'\) is:
\[ I' = \frac{I}{4} \]

5. **Finding the Percentage Difference**:
The percentage difference between the initial and final intensities can be calculated using the formula:
\[ \text{Percentage Difference} = \frac{I - I'}{I} \times 100 \]
Substituting \(I'\) into the equation:
\[ \text{Percentage Difference} = \frac{I - \frac{I}{4}}{I} \times 100 \]

6. **Simplifying the Expression**:
This simplifies to:
\[ \text{Percentage Difference} = \frac{I - \frac{I}{4}}{I} \times 100 = \frac{\frac{4I}{4} - \frac{I}{4}}{I} \times 100 = \frac{\frac{3I}{4}}{I} \times 100 \]
The \(I\) cancels out:
\[ \text{Percentage Difference} = \frac{3}{4} \times 100 = 75\% \]

### Final Answer:
The percentage difference between the initial and final intensities is **75%**.