What are coherent sources? Why are they necessary for observing a sustained interference pattern?
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Solution and Explanation
1. Coherent Sources:
Coherent sources are two or more light sources that emit waves with a constant phase relationship over time. In other words, the waves emitted by these sources maintain a fixed and predictable phase difference. There are two key types of coherence:
- Temporal Coherence: The phase difference between the waves remains constant over time. This is associated with the monochromaticity (single frequency) of the waves.
- Spatial Coherence: The phase difference between the waves remains constant across different points in space. This is associated with the uniformity of the wavefront.
2. Necessity of Coherent Sources for Sustained Interference Pattern:
Interference patterns are formed when two or more coherent waves superpose, resulting in constructive or destructive interference. For a sustained interference pattern to be observed, the following conditions must be met:
- Constant Phase Relationship: Coherent sources emit waves that maintain a constant phase relationship over time, which is necessary for constructive and destructive interference to be stable. If the phase difference between the waves changes randomly, the interference pattern will continuously shift, leading to a disappearing or fluctuating pattern.
- Same Frequency: Coherent sources must have the same frequency to ensure that the waves have a fixed relationship. If the frequencies of the sources are different, the waves will gradually lose synchronization, and the interference pattern will not remain sustained.
For example, in Young’s double-slit experiment, a sustained interference pattern can only be observed if the light coming from the two slits is coherent. If the light sources are not coherent, the interference fringes will not be stable, and the pattern will fade away.
3. Conclusion:
- Coherent sources are light sources that emit waves with a constant phase relationship over time.
- They are necessary for observing a sustained interference pattern because they ensure a stable phase difference and constant synchronization between the waves, which is essential for stable constructive and destructive interference.
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