When light falls on two polaroid sheets having their axies matually perpendicular, then it is

Options

A. completly extinguished
B. partly extinguished
C. partly brightnessed
D. completely brightnessed

Answer

To solve the question regarding the behavior of light when it passes through two polaroid sheets with their axes mutually perpendicular, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- We have two polaroid sheets (let's call them P1 and P2).
- The axis of P1 is oriented in one direction, and the axis of P2 is oriented at 90 degrees (or π/2 radians) to the axis of P1.

2. **Applying Malus's Law**:
- Malus's Law states that when polarized light passes through a polarizer, the intensity of the transmitted light (I) is given by:
\[ I = I_0 \cos^2(\theta) \]
where \(I_0\) is the intensity of the incoming light and \(\theta\) is the angle between the light's polarization direction and the axis of the polarizer.

3. **Determining the Angle**:
- Since the axes of the two polaroids are mutually perpendicular, the angle \(\theta\) between the light's polarization direction (after passing through P1) and the axis of P2 is 90 degrees (or π/2 radians).

4. **Calculating the Intensity**:
- Substituting \(\theta = \frac{\pi}{2}\) into Malus's Law:
\[ I = I_0 \cos^2\left(\frac{\pi}{2}\right) \]
- We know that \(\cos\left(\frac{\pi}{2}\right) = 0\). Therefore:
\[ I = I_0 \cdot 0^2 = 0 \]

5. **Conclusion**:
- Since the intensity of the transmitted light (I) is 0, we conclude that the light is completely extinguished when it passes through the two polaroids.

### Final Answer:
The light is completely extinguished when it passes through two polaroid sheets having their axes mutually perpendicular.

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