The path difference equivalent to a phase difference of `180^(@)` (given wavelength of wave = 2) is

Options

A. Zero
B. `lambda//2`
C. `3lambda//4`
D. `lambda`

Answer

To find the path difference equivalent to a phase difference of \(180^\circ\) when the wavelength of the wave is given as \(2\), we can follow these steps:

### Step 1: Convert the phase difference from degrees to radians
The phase difference in radians can be calculated using the conversion:
\[ \text{Phase difference in radians} = \frac{\text{Phase difference in degrees} \times \pi}{180} \]
For a phase difference of \(180^\circ\):
\[ \Delta \phi = \frac{180 \times \pi}{180} = \pi \text{ radians} \]

### Step 2: Use the formula for path difference
The path difference \(\Delta x\) corresponding to a phase difference \(\Delta \phi\) is given by the formula:
\[ \Delta x = \frac{\lambda \Delta \phi}{2\pi} \]
where \(\lambda\) is the wavelength.

### Step 3: Substitute the values into the formula
Given that the wavelength \(\lambda = 2\) and \(\Delta \phi = \pi\):
\[ \Delta x = \frac{2 \cdot \pi}{2\pi} \]

### Step 4: Simplify the expression
Now, simplify the expression:
\[ \Delta x = \frac{2\pi}{2\pi} = 1 \]

### Conclusion
The path difference equivalent to a phase difference of \(180^\circ\) is:
\[ \Delta x = 1 \]

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