The full picture is still being studied, but auxin (a plant hormone) plays a significant role. Auxin prevents cells from getting longer and the [Cholodny–Went model](https://en.wikipedia.org/wiki/Cholodny%E2%80%93Went_model?wprov=sfla1) says that the auxins move to the shady side of the growth point. The opposite cells then get longer, which bends the tip towards the light.
In the roots the auxin goes to the lower side and the other side gets longer, bending the tip down.
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