Question

why dispersion of light takes place in prism

Answer 1

If the two interface surfaces are parallel to each other, as in a 'slab' of glass, all of the bending (anddispersion) that takes place at the first interfaces is exactly reversed at the second, 'undoing' the effect of the first interface; so although the emerging ray of light is displaced slightly from the entering ...

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Answer 2

The refractive index of the material of a prism is different for different colours of light  as different colours have different speeds in the material of a prism. Also, prism has non-parallel  surfaces.