Question

Lights from two independent sources are not coherent. Explain.

Hint:

For interference to be sustained, the phase difference between the waves should remain constant, which requires the sources to be coherent.

Answer 1

1. Definition of Coherence:

Coherence refers to the correlation between the phases of two or more light waves. Two waves are said to be coherent if they have a constant phase relationship over time, meaning their phase difference remains unchanged. There are two types of coherence:

• Temporal Coherence: This refers to the consistency of phase difference between two waves at a fixed point in space as a function of time. It is related to the monochromaticity (or wavelength) of the light.
• Spatial Coherence: This refers to the consistency of phase difference between two points in space, such as at different points across a wavefront.

2. Why Light from Two Independent Sources is Not Coherent:

When light comes from two independent sources, the phases of the waves emitted by each source are random and uncorrelated with each other. This randomness leads to a lack of phase relationship between the two light waves, making them incoherent.

For two sources to produce coherent light, they must have the same frequency (temporal coherence) and maintain a fixed phase relationship (spatial coherence) over time. Since independent light sources generally emit light waves with random phases and different frequencies, the light from these sources is not coherent.

3. Example:

For example, if we have two light bulbs emitting light independently, each bulb's light wave is generated randomly, meaning that their phase difference changes constantly. This makes their light incoherent. On the other hand, in the case of a laser, light from a single source is coherent because all emitted waves have the same frequency and maintain a fixed phase relationship.

4. Conclusion:

• Light from two independent sources is not coherent because the phases of the waves from each source are random and uncorrelated.
• For coherence to exist, the sources must emit light with a consistent phase relationship over time and space.