Why does white light split into different colours when passing through a prism but not when passing through a glass slab?
Because a prism has non-parallel sides
A glass slab has two parallel refracting faces. Light bends towards the normal as it enters and by exactly the same amount away from the normal as it leaves, so the emergent ray is parallel to the incident ray and every colour is displaced equally.
A prism has two refracting faces inclined to each other, so the second refraction adds to the first instead of cancelling it.
Each colour has its own refractive index in glass (violet the highest, red the lowest), so with non-parallel faces each colour emerges along a different direction and the beam spreads out into a spectrum.
Hence, the answer is because a prism has non-parallel sides.
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