Question

Lights from two independent sources are not coherent. Explain.

Hint:

To obtain coherent sources, a single source is often split into two, such as in Young’s double-slit experiment.

Answer 1

Why Lights from Two Independent Sources Are Not Coherent

Definition of Coherence: 

Coherence refers to the property of a wave where the phase relationship between different points on the wave or between different waves remains constant over time. There are two types of coherence:

• Temporal Coherence: Refers to the consistency of phase over time. A light source with temporal coherence produces waves that maintain a fixed phase relationship over time.
• Spatial Coherence: Refers to the consistency of phase across different points in space. A light source with spatial coherence has waves that are in phase at different points in space.

Why Independent Light Sources Are Not Coherent:

Light from two independent sources is generally not coherent because of the following reasons:

• Random Phase Relationship: Independent light sources (e.g., two light bulbs or lasers from different devices) do not have a fixed phase relationship. The phases of the light waves emitted by these sources vary randomly. Thus, the phase difference between the two waves fluctuates, making them incoherent.
• Inconsistent Frequency: The frequencies of light emitted by independent sources might be slightly different, which results in a lack of temporal coherence. When the frequencies are not identical, there is no well-defined constant phase difference over time, leading to an unstable interference pattern.
• Spatial Incoherence: Since the sources are independent and not phase-locked, the light emitted from each source is not guaranteed to be in phase across different points. Hence, there is a lack of spatial coherence as well.

Example of Coherent Light:

A typical example of coherent light is the output from a single laser. In this case, the light waves are generated from a single point source and maintain a constant phase relationship both in time (temporal coherence) and across space (spatial coherence).

Conclusion:

Therefore, lights from two independent sources are not coherent due to random phase differences, possible differences in frequency, and lack of phase synchronization, which prevents them from producing stable interference patterns over time and space.