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Why are two bulbs lighting the same wall considered as incoherent sources? How do their intensities add up?

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The bulbs are incoherent sources because at any frequency, the radiation from one has no stable phase relation with the other. This is because independent atoms and electrons are responsible for the radiation for each source.

For two different frequencies, the interference term becomes zero

∴ the intensities of two bulbs get added up.

i.e., I = I1 + I2.

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