Coherent Sources and the Condition for Sustained Interference

When light waves from two (or more) sources overlap in a region of space, the resultant intensity at any point depends on the phase relationship between the waves arriving there, a phenomenon called interference. If the two sources have the same frequency and either exactly zero or some other constant phase difference between them at all times, they are said to be coherent, and the interference pattern they produce -- a fixed spatial arrangement of bright and dark regions -- remains stationary in time, i.e. is sustained, and hence observable.

Two genuinely independent light sources -- even two identical sodium vapour lamps -- can never be coherent in practice, because each source's atoms emit light in short, random bursts, so the phase difference between the two sources' output fluctuates completely randomly, typically many times within a nanosecond. Any resulting interference pattern shifts position just as fast, far too fast for the eye or any ordinary detector to follow, so only a time-averaged uniform illumination is seen, with no fringes at all. A sustained pattern is therefore only ever obtained by deriving both interfering beams from a single source, so that any random phase change in the original source affects both derived beams identically and their relative phase relationship stays fixed. Young's double sl …