Usually rainbows are present after the rain. But if a rainbow is caused by diffraction of rain droplets, shouldn't rainbows be present during the rain, not after?
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The rainbow needs sun and rain. Normally during the rain there is no sunlight.
After the rain there is generally still rainfall but it has moved away. If the sun has come out where you are and strikes the rain that is moving away from you at the right angle then you will see a rainbow.
rainbow reference for more details.

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