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

Incoherence of Light from Two Independent Sources

Coherence Defined:

Coherence describes a wave's characteristic where the phase relationship between different points on the wave or between multiple waves remains consistent over time. Two primary types of coherence exist:

• Temporal Coherence: This pertains to phase consistency over time. A temporally coherent light source emits waves that sustain a fixed phase relationship throughout their duration.
• Spatial Coherence: This relates to phase consistency across different spatial locations. A spatially coherent light source exhibits waves that are in phase at various points in space.

Reasons for Incoherence in Independent Light Sources:

Light originating from two independent sources typically lacks coherence due to the following factors:

• Unpredictable Phase Relationship: Independent light sources (such as separate light bulbs or lasers from distinct devices) do not possess a fixed phase relationship. The phases of the light waves they emit fluctuate randomly. Consequently, the phase difference between the two waves varies unpredictably, rendering them incoherent.
• Variable Frequencies: Slight differences in the frequencies of light emitted by independent sources can lead to a deficit in temporal coherence. When frequencies are not identical, a stable, constant phase difference over time does not exist, resulting in an unstable interference pattern.
• Spatial Disarray: As the sources are independent and not synchronized in phase, the light emitted by each is not guaranteed to be in phase across different spatial points. This results in a deficiency in spatial coherence.

Example of Coherent Light:

A common illustration of coherent light is the output from a single laser. In such a scenario, the light waves originate from a singular point source and maintain a constant phase relationship both temporally (temporal coherence) and spatially (spatial coherence).

Summary:

In conclusion, light from two independent sources is rendered incoherent by random phase variations, potential frequency disparities, and an absence of phase synchronization. These factors preclude the formation of stable interference patterns across time and space.