The phase difference corresponding to path difference of x is

Options

A. `(2pix)/(lamda)`
B. `(2pilamda)/(x)`
C. `(pix)/(lamda)`
D. `(pilamda)/(x)`

Explanation

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

### Step 1: Understand the relationship between phase difference and path difference
The phase difference \( \Delta \phi \) is related to the path difference \( \Delta y \) by the formula:
\[ \Delta \phi = k \Delta y \]
where \( k \) is the wave number.

### Step 2: Define the wave number \( k \)
The wave number \( k \) is defined as:
\[ k = \frac{2\pi}{\lambda} \]
where \( \lambda \) is the wavelength of the wave.

### Step 3: Substitute the path difference into the phase difference formula
Given that the path difference \( \Delta y = x \), we can substitute this into the phase difference formula:
\[ \Delta \phi = k \cdot x \]

### Step 4: Substitute the value of \( k \)
Now, substituting the value of \( k \) into the equation:
\[ \Delta \phi = \left(\frac{2\pi}{\lambda}\right) \cdot x \]

### Step 5: Write the final expression for phase difference
Thus, the phase difference corresponding to a path difference of \( x \) is:
\[ \Delta \phi = \frac{2\pi x}{\lambda} \]

### Final Answer
The phase difference corresponding to a path difference of \( x \) is:
\[ \Delta \phi = \frac{2\pi x}{\lambda} \]

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