To demonstrate the phenomenon of interference, we require two sources which emit radiation

Options

A. nearly the same frequency
B. the same frequency
C. different wavelength
D. the same frequency and having a definite phase relationship

Answer

To solve the question regarding the requirements for demonstrating the phenomenon of interference, we need to analyze the options provided and understand the concept of coherent sources.

### Step-by-Step Solution:

1. **Understanding Interference**:
- Interference is a phenomenon that occurs when two or more waves overlap and combine to form a new wave pattern. For this to happen effectively, the sources of these waves must have certain characteristics.

2. **Identifying Coherent Sources**:
- Coherent sources are defined as sources that emit waves with the same frequency and a constant phase difference. This means that the waves produced by these sources will maintain a consistent relationship over time, which is essential for producing a stable interference pattern.

3. **Analyzing the Options**:
- **Option A**: "Nearly the same frequency" - This does not guarantee coherence, as the frequencies must be exactly the same.
- **Option B**: "The same frequency" - This is a requirement, but it does not mention the phase relationship.
- **Option C**: "Different wavelength" - This is incorrect because different wavelengths imply different frequencies, which would not be coherent.
- **Option D**: "The same frequency and having a definite phase relationship" - This option correctly states the requirements for coherent sources.

4. **Conclusion**:
- Based on the analysis, the correct answer is **Option D**: "The same frequency and having a definite phase relationship". This option fulfills both criteria necessary for demonstrating interference.

### Final Answer:
The correct answer is **Option D**: The same frequency and having a definite phase relationship.

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