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If you know the explanation for why the sky's blue, you've heard that sunlight is white
light composed of many frequencies and that higher frequency, bluer, light scatters in
the air more than lower frequency, redder, light.
So, you might ask "why isn't the sky violet, since violet is an even higher frequency than
blue?".
First off, ultraviolet light and x-rays are also higher frequency than blue, and that
doesn't mean the sky is the color of x-rays…
Both because we can't see them and also because the sun doesn't make very many of them and
then the atmosphere blocks them all - which is probably why we didn't evolve to be able
to see them.
And secondly, the color violet in the rainbow is the "roses are red, violets are BLUE" violet.
Not purple – it's dark blue.
To see why, check out this Chromaticity Diagram!
It's a graph of all possible colors as perceived by non-colorblind humans, ignoring brightness
and context.
The color displayed on the diagram is just to give you a rough idea – unfortunately
your computer can't display all possible perceived colors – it can just display the ones inside
a triangle like this, and is pretending for the rest.
Single frequency light like that from a laser or from splitting white light into a rainbow
is graphed around this outside edge, while any color anywhere on the inside or along
the bottom edge can only be made with a combination of various frequencies of light.
As you can see, pink, purple and magenta can only be made using multiple frequencies of
light - there is no single frequency of light that's pink - and of course, white light is
a mixture as well!
Which is why you don't see any of these colors in rainbows made from prisms.
But back to the Chromaticity diagram!
See this line in the middle?
This shows what color hot objects glow - we have red hot, then white hot, then blue hot.
All of these "hot" colors are made up of a broad range of frequencies, since that's what
hot objects emit.
The sun, for example, is white hot before it hits the atmosphere, then its light is
split by scattering off of air molecules so the sun looks slightly red hot and the rest
of the sky looks kind of blue hot.
Like this picture of a sunset!
And the thing is this - if you notice the line for hot-object color, well, it stops
in the middle of the diagram near whitish-blue.
It never goes beyond that.
And that's because the spectrum of light from an object hotter than the sun always has a
decreasing tail, with slightly more blue than green than red, so you never get the right
combination of frequencies to push the color towards purple, or for that matter, even towards
a pure, deep violet blue.
Kind of like how you can mix flour and water in different ratios to make bread, pancakes,
or vegetarian gravy, but as long as you have flour in there, your gravy won't be gluten
free.
And that's why the sky appears blueish white.
It's basically gravy.