Two light sources are coherent when

Options

A. their amplitudes are equal
B. their frequencies are equal
C. their wavelengths are equal
D. their frequencies are equal their phase difference is constant with time

Answer

To determine the conditions under which two light sources are coherent, we can break down the explanation into clear steps:

### Step-by-Step Solution:

1. **Definition of Coherent Sources**:
Coherent sources are defined as light sources that maintain a constant phase relationship. This means that the light waves emitted from these sources should have a fixed phase difference over time.

**Hint**: Remember that coherence is all about the phase relationship between the waves.

2. **Single Source Division**:
To create coherent sources, we can use a single light source and split it into two. This can be done by using two small openings (slits) in a barrier. The light waves emanating from these slits will be coherent if they originate from the same wavefront.

**Hint**: Think about how splitting a single wavefront can lead to two coherent sources.

3. **Frequency Condition**:
For two light sources to be coherent, they must have the same frequency. Since frequency is determined by the source, if both sources are derived from the same original source, they will have the same frequency.

**Hint**: Frequency is a key characteristic of waves; it must be identical for coherence.

4. **Wavelength Consideration**:
The wavelength of the light may or may not be the same, depending on the medium through which the light travels. However, if the frequency is the same, the wavelengths will be consistent with the medium's properties.

**Hint**: Wavelength can change with the medium, but frequency remains constant for coherence.

5. **Constant Phase Difference**:
The phase difference between the two sources must remain constant over time. This means if there is an initial phase difference (φ), it should not change as time progresses.

**Hint**: A constant phase difference is crucial for maintaining coherence.

6. **Conclusion**:
Therefore, the conditions for two light sources to be coherent are:
- They must have the same frequency.
- The phase difference between the two sources must be constant over time.

**Hint**: Summarize the conditions: same frequency and constant phase difference.

### Final Answer:
Two light sources are coherent when they have the same frequency and a constant phase difference over time.