How does a glass prism separate white light into a spectrum of colours?

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A glass prism separates white light into a spectrum of colours through a process called dispersion.

When light passes from air into the glass of the prism, it undergoes refraction, or bending. The degree of this bending depends on the refractive index of the glass, which varies for different wavelengths of light. Because white light is composed of various wavelengths, each colour is bent at a slightly different angle as it enters and exits the prism.123

Specifically, shorter wavelengths—such as those toward the violet end of the spectrum—are refracted the most, while longer wavelengths—such as those toward the red end—are refracted the least. This differential bending causes the incident beam of white light to fan out, effectively spreading the light into its constituent colours. This phenomenon is also known as angular or chromatic dispersion.123