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The basic cause of the color is atmospheric dispersion: refraction by air is larger at shorter wavelengths. So, at sunset, the refractive delay of the sunset is usually a second or two longer for blue and violet than for red. In general, then, the red image of the Sun (or of some miraged part of it) sets or disappears first, followed by yellow, green, blue and violet.
So why isn't violet the last color to be seen at sunset? There is another effect at work: atmospheric extinction. Both air molecules and aerosol particles scatter the shortest wavelengths most strongly (which is why the sky is blue: the strongly-scattered blue light goes in all directions, so we see it when we look anywhere in the sky). At the horizon, the path length through the air is very long, and the shortest wavelengths are almost completely removed.
The classical green flash, a brilliant glint of green almost on the ocean horizon just as the sun disappears, relies on a mirage to magnify the usually small differences in refraction between red and green light. The mirage occurs when there is warm air immediately over the ocean and the air temperature gradient changes rapidly with height, i.e. the temperature profile is curved. For the flash to be visible the warm air layers must be below you.
First indications of something unusual are when a sliver of a 'second sun' rises from the horizon as the 'real sun' descends. The lower sun is an inferior mirage (inferior because the image is below the real sun). As the sunset proceeds the lower sun eventually links with the upper sun to form an Etruscan vase or omega shape. The two suns overlap more and more. At the moment when the suns are almost gone the vertical magnification between the different paths of green and red rays is strongest. The green flash then shines forth.
There is a distinct, but related, phenomenon that really deserves the term “flash.” In this much rarer display, a green flash of the ordinary kind is followed (at sunset) by a brief ray or glow of green, which often appears to shoot up from the sunset point. It often accompanies, or follows, a “green dot”. These very rare displays are grouped under the term “green ray,” although the ray form is only one of several. Unfortunately, the term “green ray” has often been applied to the much commoner green-flash displays of the “green dot” form.