What happens to frequency during dispersion?

Question

I'm a bit confused about what happens to frequency during the dispersion of white light passing through a prism. I understand that when a light wave is travelling in  one medium, velocity is constant and frequency and wavelength vary inversely. I then read that when waves change mediums, frequency remains constant while velocity and wavelength vary directly. How does this work? Doesn't frequency need to change for the different colors (ROY G. BIV) of visible light to appear?

Gilbert · Answer

White light contains a wide range of frequencies which remain constant from medium to medium. Wavelength and velocity change according to the refractive index. In a prism, different refractive indices for different colors (“dispersion”) cause refraction at different angles, so the components of the white light become individuality visible.

Answered by Gilbert on August 26, 2021

What happens to frequency during dispersion?

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