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 describes the correlation in the phases of multiple light waves. Two waves are considered coherent if their phase difference remains constant over time. Coherence is categorized into two types:

• Temporal Coherence: This refers to the stability of the phase difference between two waves at a single point in space, observed over time. It is linked to the light's monochromaticity (wavelength).
• Spatial Coherence: This refers to the stability of the phase difference between different points in space, such as across a wavefront.

2. Incoherence of Light from Two Independent Sources:

Light originating from two independent sources exhibits random and uncorrelated phases for the emitted waves. This lack of correlation prevents a stable phase relationship, resulting in incoherent light.

For light to be coherent, sources must emit waves with identical frequencies (temporal coherence) and maintain a fixed phase relationship (spatial coherence) over time. Since independent sources typically produce waves with random phases and varying frequencies, their combined light is incoherent.

3. Illustrative Example:

Consider two light bulbs operating independently. The light waves from each bulb are generated randomly, leading to a continuously changing phase difference and thus incoherence. In contrast, laser light, originating from a single source, is coherent because all emitted waves share the same frequency and maintain a consistent phase relationship.

4. Summary:

• Light from two independent sources is incoherent due to the random and uncorrelated phases of their emitted waves.
• Coherence requires sources to produce light with a stable phase relationship across time and space.