The coherent sources of light produce constructive interference when phase difference between them is

Options

A. `pi`
B. `(pi)/2`
C. `(3pi)/2`
D. `2pi`

Explanation

To determine the phase difference required for constructive interference between two coherent light sources, we can follow these steps:

### Step 1: Understand the Condition for Constructive Interference
Constructive interference occurs when the waves from the two coherent sources are in phase. This means that the phase difference (φ) between the two waves must be such that they reinforce each other.

### Step 2: Identify the Mathematical Condition
The mathematical expression for the amplitude of the resulting wave when two waves interfere is given by:
\[ A_{\text{net}}^2 = A_1^2 + A_2^2 + 2A_1 A_2 \cos(\phi) \]
To achieve constructive interference, we need to maximize the term \( \cos(\phi) \).

### Step 3: Determine the Maximum Value of Cosine
The maximum value of \( \cos(\phi) \) is 1. This occurs when:
\[ \phi = 0, 2\pi, 4\pi, \ldots \]
In general, we can express this as:
\[ \phi = 2n\pi \]
where \( n \) is any integer (0, 1, 2, ...).

### Step 4: Conclusion
Thus, for constructive interference, the phase difference between the two coherent sources must be:
\[ \phi = 2n\pi \]
This means the phase difference can be any even multiple of \( \pi \).

### Final Answer
The coherent sources of light produce constructive interference when the phase difference between them is \( 2n\pi \) (where \( n \) is an integer).

---