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Light is emitted due to the de-excitaton of electrons from higher orbits of the various atoms of the light source.The de-excitation can also be to different levels in different atoms resulting in emission of different wavelengths.A light source will have numerous atoms in it.When you take two light sources it is not possible for all the atoms to get de-excited to the same shell at the same time(causing phase difference) that is why two independent sources cannot be coherent.

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Q: Why two independent sources cannot behave as a coherent sources?
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