Coherence (definition)
● VERBATIM — examined word-for-wordTwo waves or sources are coherent if there is a constant phase difference between them. This requires them to have the same frequency (and hence the same wavelength in a given medium). Coherent does not mean in phase, and does not require equal amplitudes.
What this actually means
Constant, not zero. Two sources with a permanent phase difference of π/2 are perfectly coherent. Students who write coherent means in phase throw away the mark.
Same frequency follows automatically: if the frequencies differed, the phase difference would grow steadily with time and could not be constant.
Two independent lamps, or two independent lasers, are not coherent. Light from an ordinary source undergoes a random phase change roughly every 10⁻⁸ s, so any interference pattern reshuffles far faster than the eye can follow and averages out.
The standard fix is to make both beams come from the same original wave. Division of wavefront (a single slit feeding a double slit) or division of amplitude (a partly reflecting mirror) both work.
Two loudspeakers wired to one signal generator are coherent because both are driven by the same oscillation. Two separate signal generators set to the same nominal frequency are not, because they drift.
Writing that coherent sources must be in phase, when the requirement is only a constant phase difference.
Prove it — watch it be true
- Use the coherence-breaking toggle to randomise the phase of the second source.
- Watch the screen intensity profile lose its fringes and settle into a uniform glow.
- Set a fixed non-zero phase offset instead and confirm sharp fringes return, just shifted sideways.