When light falls on two polaroid sheets, one observes complete brightness then the two polaroids axes are

Options

A. mutually perpendicular
B. mutually parallel
C. angle between their two axes is `45^(@)`
D. none of the above

Answer

To solve the problem regarding the brightness observed when light passes through two polaroid sheets, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Polaroids**:
- A polaroid sheet allows light waves oscillating in a particular direction (the axis of the polaroid) to pass through while blocking light waves oscillating in other directions.

2. **Identifying the Polaroids**:
- Let's denote the first polaroid as the "polarizer" and the second one as the "analyzer". The axis of the polarizer is aligned in a certain direction, and the axis of the analyzer can be at an angle θ with respect to the polarizer.

3. **Applying Malus's Law**:
- According to Malus's Law, the intensity of light (I) passing through the analyzer is given by:
\[ I = I_0 \cos^2(\theta) \]
where \(I_0\) is the intensity of light after passing through the first polaroid (the polarizer), and θ is the angle between the axes of the polarizer and the analyzer.

4. **Condition for Complete Brightness**:
- For complete brightness to be observed after passing through both polaroids, the intensity \(I\) must equal the intensity \(I_0\). This means:
\[ I = I_0 \Rightarrow I_0 \cos^2(\theta) = I_0 \]

5. **Simplifying the Equation**:
- Dividing both sides by \(I_0\) (assuming \(I_0 \neq 0\)):
\[ \cos^2(\theta) = 1 \]

6. **Finding the Angle θ**:
- The equation \(\cos^2(\theta) = 1\) implies that:
\[ \cos(\theta) = 1 \]
- This occurs when:
\[ \theta = 0^\circ \quad \text{or} \quad \theta = 360^\circ \]
- Therefore, the axes of the two polaroids must be **mutually parallel**.

### Conclusion:
When light falls on two polaroid sheets and complete brightness is observed, the axes of the two polaroids are **mutually parallel**.