Q.What are different types of dispersions of light? Why do they occur?

[!TLDR] Dispersion is angular (colours fan out at a single surface, e.g. a prism) or lateral (colours stay parallel but shift sideways, e.g. a slab); both occur because refractive index -- and hence bending -- differs by colour/frequency. [!ANSWER] Angular dispersion (single surface, colours separate by angle) and lateral dispersion (slab, colours separate by parallel offset); both caused by refractive index increasing with frequency.

A material's refractive index depends on the frequency of the light passing through it, increasing with frequency -- so violet light (highest visible frequency) bends more than red (lowest visible frequency) at every ordinary refracting interface. Because of this, whenever a beam containing multiple colours refracts obliquely, each colour bends by a different amount and the colours physically separate: this splitting is DISPERSION, and it occurs in two geometrically distinct forms depending on the shape of the refracting element. ANGULAR DISPERSION occurs at a SINGLE refracting surface (or through a prism, whose two surfaces are inclined, not parallel): the different colours genuinely diverge at different ANGLES from one point, fanning outward -- easily visible, and the basis of how a prism spreads white light into a spectrum. LATERAL DISPERSION occurs when light passes through a plane-PARALLEL slab: because the two surfaces are exactly parallel, every emergent colour ends up travelling in the SAME final direction as the others (and as the original incident beam) -- but the different colours are laterally OFFSET from one another and from the undeviated straight-through path, a much smaller, harder-to-detect effect requiring a large slab thickness and large angle of incidence to become measurable at all. Both forms occur for the SAME underlying reason (colour-dependent refractive index); they differ only in the GEOMETRY of the refracting element (inclined surfaces versus parallel surfaces), which determines whether the separated colours end up travelling in different final directions (angular) or the same final direction but offset (lateral). [!ANSWER] Angular dispersion (inclined surfaces, e.g. prism -- colours separate by direction) and lateral dispersion (parallel surfaces, e.g. slab -- colours stay parallel but shift sideways); both occur because refractive index increases with frequency, so different colours bend by different amounts.

Explain the common physical cause (frequency-dependent refractive index) first, then distinguish the two dispersion types by the GEOMETRY of the refracting element (inclined vs parallel surfaces) and what that geometry does to the separated colours' final directions.

Describing only one type of dispersion (usually angular, via a prism) and omitting lateral dispersion (via a slab) as a genuinely distinct, separately named case.