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In Youngâ??s double slit experiment, the two slits are illuminated by two different lamps having same wavelength of light. Explain with reason, whether interference pattern will be observed on the screen or not.

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In principle you will not. Because even if the wavelengths of the emitting light from the two sources are same there is no definite relationship between the phases of the two. This makes the lights passing through the two slits incoherent, which is a necessary criterion for interference.
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