In a wave, the path difference corresponding to a phase difference of `phi` is

Options

A. `pi/(2lambda) phi`
B. `pi/lambda phi`
C. `lambda/(2pi) phi`
D. `lambda/pi phi`

Answer

To find the path difference corresponding to a phase difference of \( \phi \), we can follow these steps:

### Step 1: Understand the relationship between phase difference and wavelength
The phase difference \( \phi \) in a wave is related to the path difference \( \Delta x \) by the equation:
\[ \phi = \frac{2\pi}{\lambda} \Delta x \]
where \( \lambda \) is the wavelength of the wave.

### Step 2: Rearranging the equation
We can rearrange the equation to express the path difference \( \Delta x \) in terms of the phase difference \( \phi \):
\[ \Delta x = \frac{\lambda}{2\pi} \phi \]

### Step 3: Final expression
Thus, the path difference corresponding to a phase difference of \( \phi \) is given by:
\[ \Delta x = \frac{\lambda}{2\pi} \phi \]

### Conclusion
The path difference corresponding to a phase difference of \( \phi \) is \( \frac{\lambda}{2\pi} \phi \).

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