In Young's double slit experiment, if the two slits areilluminated with separate sources, no interference pattern is observed because

In conventional light source, light comes from a large number of independent atoms, each atom emitting light for about 10-9 sec i.e. light emitted by an atom is essentially a pulse lasting for only 10-9 sec. Light coming out from two slits will have a fixed phase relationship only for 10-9 sec. Hence any interference pattern formed on the screen would last only for 10-9 sec, and then the pattern will change. The human eye can notice intensity changes which last at least for a tenth of a second and hence we will not be able to see any interference pattern. In stead due to rapid changes in the pattern, we will only observe a uniform intensity over the screen.

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