Two light sources are said to be coherent if they emit :

Question

Accepted Answer

To understand why Option 3 is the correct answer, we need to delve into the concept of coherence in the context of wave physics, particularly in optics.

1. **Explanation for Option 3 (Correct Answer): Waves having constant phase difference**

Coherence refers to a fixed relationship between the phase of waves in a beam of radiation of a single frequency. Two light sources are said to be coherent if they emit waves that maintain a constant phase difference over time. This means that the peaks and troughs of the waves from the two sources align consistently, which is crucial for producing stable interference patterns. This constant phase relationship is what allows coherent light sources to produce clear and stable interference patterns, which are essential in applications like holography and interferometry.

2. **Explanation for why the other options are incorrect:**

- **Option 1: Light of same intensity**

Intensity refers to the power per unit area carried by a wave. While having the same intensity might be desirable in some applications for uniformity, it does not define coherence. Coherence is about the phase relationship between waves, not their intensity. Two light sources can have different intensities and still be coherent if they maintain a constant phase difference.

- **Option 2: Waves of same frequency**

While having the same frequency is a necessary condition for coherence, it is not sufficient on its own. Two waves can have the same frequency but still be incoherent if their phase relationship is random or varies over time. Coherence requires both the same frequency and a constant phase difference.

- **Option 4: Waves of same velocity**

The velocity of light waves in a given medium is generally constant and does not affect coherence. Coherence is concerned with the phase relationship between waves, not their speed. Therefore, having the same velocity does not ensure coherence.

In summary, coherence is fundamentally about the phase relationship between waves. Option 3 correctly identifies that coherence requires waves to have a constant phase difference, which is essential for producing stable interference patterns. This is why Option 3 is the correct answer.