The phase difference between two points `A` and `B` on a wavefront separated by distance `lambda` is

Options

A. `0`
B. `2 pi`
C. `pi`
D. `pi//2`

Answer

To find the phase difference between two points A and B on a wavefront separated by a distance of one wavelength (λ), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Phase Difference**:
The phase difference (Δφ) between two points on a wavefront can be expressed in terms of the distance between those points and the wavelength of the wave.

2. **Use the Formula for Phase Difference**:
The phase difference is given by the formula:
\[ \Delta \phi = k \cdot x \]
where \( k \) is the wave number and \( x \) is the distance between the two points.

3. **Determine the Wave Number (k)**:
The wave number \( k \) is defined as:
\[ k = \frac{2\pi}{\lambda} \]
where \( \lambda \) is the wavelength of the wave.

4. **Substitute the Distance**:
In this case, the distance \( x \) between points A and B is given as \( \lambda \). Therefore, we can substitute \( x \) in the phase difference formula:
\[ \Delta \phi = k \cdot \lambda \]

5. **Calculate the Phase Difference**:
Now substituting the value of \( k \):
\[ \Delta \phi = \left(\frac{2\pi}{\lambda}\right) \cdot \lambda \]
The \( \lambda \) in the numerator and denominator cancels out:
\[ \Delta \phi = 2\pi \]

6. **Interpret the Result**:
A phase difference of \( 2\pi \) radians corresponds to a complete cycle of the wave. This means that points A and B are in phase, and there is effectively no difference in their phase. In terms of degrees, \( 2\pi \) radians is equivalent to \( 360^\circ \).

### Final Answer:
The phase difference between points A and B separated by a distance of \( \lambda \) is \( 2\pi \) radians (or \( 360^\circ \)), which indicates that they are in phase.

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