Q.State the two conditions that two light sources must satisfy to be called coherent sources, and explain why coherence is essential for a sustained interference pattern to be observed.

Two sources are called coherent if they satisfy two conditions together: they must emit waves of exactly the same frequency (and hence the same wavelength, in the same medium), and the phase difference between the two waves, at any given point, must remain constant in time (it need not be zero, just unchanging).

Coherence is essential for a sustained interference pattern because the position of every bright or dark fringe is fixed by the phase difference between the two waves at that point. If the phase difference between the two sources itself keeps changing randomly (as it does for two independent sources), then the positions of constructive and destructive interference shift correspondingly, and if this happens fast enough (as it does in practice, on a nanosecond timescale for ordinary light sources), the eye or detector only registers a rapid, time-averaged blur -- a uniform illumination with no visible fringes at all. Only when the phase difference is held fixed (as achieved by deriving both beams from a single source, e.g. via Young's two slits) do the positions of the bright and dark regions stay put, producing a pattern that can actually be seen and measured.

State both defining conditions for coherence, then link a fluctuating phase difference to a fluctuating (hence unobservable) fringe pattern.

• Stating only 'same frequency' as the condition for coherence and omitting the constant-phase requirement.
• Saying incoherent sources produce 'no interference' rather than an interference pattern that changes too fast to be observed.