Q.Explain why two independent sodium vapour lamps, even though they emit light of the same wavelength, cannot produce a sustained (observable) interference pattern, while the two slits of a Young's double slit set-up illuminated by a single source can.

Two light sources produce a sustained (stationary, observable) interference pattern only if they are coherent, i.e. they have the same frequency and a phase difference between them that stays constant in time.

Two separate sodium lamps, even of the identical wavelength, are each made up of enormous numbers of atoms emitting light independently, in short random bursts lasting only nanoseconds. The phase relationship between the light coming from lamp 1 and from lamp 2 therefore itself changes randomly, many times each nanosecond. Any interference pattern this would produce shifts position just as fast, far too quickly for the eye or any practical detector to register, so only a smeared-out, uniform (time-averaged) illumination is seen -- no fringes. …

Compare how the relative phase between the two sources behaves over time: random and fast (independent lamp …

• Thinking 'same wavelength' is enough for coherence -- it is necessary but not sufficient; the phase relationship must also stay constant. …