Coherent Sources — Definition

Definition

Imagine two friends trying to clap their hands in sync. If they start clapping at exactly the same moment and maintain the same rhythm and speed, their claps will always be in sync – they are 'coherent' in their clapping. If one friend speeds up or slows down randomly, or starts at a different time, their claps will quickly become out of sync – they are 'incoherent'.

In physics, specifically with light waves, 'coherent sources' are like those perfectly synchronized friends. They are two or more sources of light that emit waves with a constant phase difference between them.

This means that if at one point in time, the crest of a wave from source A aligns with the crest of a wave from source B, they will continue to align in the same way (or always be out of sync by the same amount, like one always clapping half a beat after the other) at all subsequent times.

For this constant phase difference to exist, two crucial conditions must be met:

1
Same Wavelength and Frequency (Monochromaticity): — The waves emitted by coherent sources must have the exact same wavelength ($lambda$) and, consequently, the same frequency ($f$). If the frequencies were different, their relative phase would continuously change, making it impossible to maintain a constant phase difference. Think of two clocks ticking at slightly different rates; eventually, they will drift apart.
2
Constant Phase Difference: — The phase difference ($Deltaphi$) between the waves from the two sources must remain constant over time. It doesn't have to be zero (meaning they are perfectly in phase), but it must not change randomly. If it changes randomly, the points of constructive and destructive interference will shift rapidly, and our eyes (or any detector) will only perceive an average, uniform illumination, not a distinct interference pattern.

Why is this important? When light waves from two coherent sources meet, they superimpose. If they are coherent, their superposition leads to stable regions where waves consistently add up (constructive interference, producing bright fringes) and stable regions where they consistently cancel out (destructive interference, producing dark fringes).

This results in a visible, sustained interference pattern. Without coherence, these patterns would flicker and vanish, leaving only a uniform brightness. This is why you don't see interference patterns from two separate light bulbs – they are incoherent sources.