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. **Understand the Problem**: We have plane polarized light incident normally on a tourmaline plate. The electric field vector (E vector) of the light makes an angle of \(60^\circ\) with the optic axis of the plate.

2. **Use Malus's Law**: According to Malus's Law, when polarized light passes through a polarizer, the intensity of the transmitted light \(I\) is given by:
\[ I = I_0 \cos^2(\phi) \]
where \(I_0\) is the initial intensity of the light and \(\phi\) is the angle between the light's electric field vector and the optic axis of the polarizer.

3. **Identify the Values**: In our case:
- Initial intensity \(I_0\)
- Angle \(\phi = 60^\circ\)

4. **Calculate the Final Intensity**:
\[ I = I_0 \cos^2(60^\circ) \]
We know that \(\cos(60^\circ) = \frac{1}{2}\), so:
\[ I = I_0 \left(\frac{1}{2}\right)^2 = I_0 \cdot \frac{1}{4} \]

5. **Calculate the Percentage Difference**:
The percentage difference between the initial intensity \(I_0\) and the final intensity \(I\) is given by:
\[ \text{Percentage Difference} = \frac{I_0 - I}{I_0} \times 100 \]
Substituting \(I\) from the previous step:
\[ \text{Percentage Difference} = \frac{I_0 - \frac{I_0}{4}}{I_0} \times 100 \]
Simplifying this:
\[ = \frac{I_0 - \frac{I_0}{4}}{I_0} \times 100 = \frac{I_0 \left(1 - \frac{1}{4}\right)}{I_0} \times 100 \]
\[ = \left(1 - \frac{1}{4}\right) \times 100 = \frac{3}{4} \times 100 = 75\% \]

6. **Final Result**: The percentage difference between the initial and final intensities is \(75\%\).