So why do synthetic dyes have such great colours? Apparently, it is because the organic (carbon-based) molecules have "conjugation". This is going to take some unpacking but it essentially means that the electron energy levels from quantum physics are modified by the combination of atoms in the molecule so that the energy difference between the highest and the lowest level is reduced to a level consistent with the visible colours in the electromagnetic spectrum. This is going to take some more work on Molecular Orbital Theory.
