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Dispersion of light is defined as the phenomena of splitting up of composite light into its constituent colours or it is deviation of different constituent parts of a composite light when the light passes through a prism.

The important point here is that the different colour deviate differently and the reason behind is that, dispersion is based on refraction of the composite light and refraction is a phenomenon based on the incident and refractive angles and refractive indices.

The deviation/refraction is find out from the Snell's law which states that the ratio of the sines of the angles of incidence and refraction of a wave are constant when it passes between two given media.

That is mathematically,

where n₁ and n₂ are refractive indexes of the medium.

The refractive index of the medium is dependent on wavelength of the light used.

So, the series go on like this,

Hence different colour light have different wavelengths resulting in different deviation angle of components of a single composite light.

Also, violet colour light has minimum wavelength while have maximum deviation this implies that wavelength is inversely proportional to the deviation angle.