A polaroid is placed at `45^(@)` to an incoming light of intensity `I_(0)` Now, the intensity of light passing through polaroid after polarization would be

Options

A. `I_(0)`
B. `I_(0)//2`
C. `I_(0)//4`
D. zero

Explanation

To find the intensity of light passing through a polaroid placed at an angle of \( 45^\circ \) to the incoming light of intensity \( I_0 \), we can use Malus's law. The law states that the intensity \( I \) of polarized light after passing through a polarizer is given by:

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

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

### Step-by-Step Solution:

1. **Identify the given values**:
- Incoming light intensity, \( I_0 \)
- Angle \( \theta = 45^\circ \)

2. **Apply Malus's Law**:
- The formula to calculate the transmitted intensity through the polaroid is:
\[ I = I_0 \cos^2 \theta \]

3. **Substitute the angle into the formula**:
- Since \( \theta = 45^\circ \):
\[ I = I_0 \cos^2(45^\circ) \]

4. **Calculate \( \cos(45^\circ) \)**:
- We know that:
\[ \cos(45^\circ) = \frac{1}{\sqrt{2}} \]

5. **Substitute \( \cos(45^\circ) \) into the formula**:
\[ I = I_0 \left(\frac{1}{\sqrt{2}}\right)^2 \]

6. **Simplify the expression**:
\[ I = I_0 \cdot \frac{1}{2} \]

7. **Final result**:
\[ I = \frac{I_0}{2} \]

Thus, the intensity of light passing through the polaroid after polarization is \( \frac{I_0}{2} \).