If the sky is blue because shorter wavelengths scatter better, why isn't it violet?

The explanation I have always heard for why the sky is blue is that the particles in the atmosphere scatter sunlight, and the shorter the wavelength the greater the scattering–hence, blue not red. But violet has an even shorter wavelength than blue, and by that theory ought to scatter even better. So why isn’t the sky violet?

There isn’t as much violet light as blue light in sunlight to scatter, and your eyes aren’t very sensitve to violet wavelengths anyway.
See this page, especially the section
‘Why not violet?’

You’re close. Matter absorbs and re-emits light. It just so happens that our atmosphere has a composition that absorbs most of the sun’s light, but the blue wavelengths get scattered more than other reflected (re-emitted) light.

The sky can be all colors, actually. Red, orange, yellow or gold, green, and yes, even violet. But these colors present themselves more when the sunlight has to cut through much more atmosphere! Like a prism, such as at sun rise, sun set, or during heavy weather conditions.

Furthermore, our atmosphere is far more opaque to UV and IR radiation than visible light. If it weren’t, you’d need sunblock 5,000 to sit poolside, and some major air conditioning.

About 15 minutes before sunrise, the sky looks quite violet to me. This was one of the really startling things I noticed after my cataract operations. In fact, after the first eye was operated on, it looked violet in that eye and yellow in the other. Now both eyes see violet then. I assume the same thing happens 15 minutes after sunset, but that direction is blocked in my house.

That’s interesting. You may be seeing some UV light, which colours your perception of the sky. If everybody had the same sensitivity, we would all see the sky with a violet tint at times. This shows that the sensitivity of the eye (and the transparency of the eye’s lens) to various wavelengths is very important.

Surely the reds and oranges and even violets that you see at sunrise/sunset have more to do with refraction than with scattering.

But is the OP’s premise that shorter wavelengths scatter more actually true? I would suggest that which wavelengths scatter the most depends on the composition of the medium doing the scattering, and it so happens that Earth’s atmosphere is so composed that it scatters blue wavelengths much more than it does red, yellow, or violet ones.

Refraction doesn’t really have much to do with it, as far as I can determine.

Rayleigh scattering is the main reason that the sky is blue on Earth. In fact the effect was discovered first by John Tyndall, when he shone a light through a weak solution of milk producing a bluish tint. Both he and Lord Rayleigh apparently thought that the blue colour in the sky was caused by tiny suspended particles in the air, but even in pure, clean air with no particulates the sky is still blue.

It was Einstein who eventually worked out that the tiny molecules of oxygen and nitrogen in the air were sufficiently good at scattering blue light that they were responsible for the colour of the sky; in so-called Rayleigh scattering, light is scattered according to the fourth power of the wavelength, so blue (and as the OP pointed out, violet) light is scattered much, much more strongly than longer wavelengths.

Yes, the lens of the eye is increasingly opaque to violet and ultraviolet as it ages and yellows. The retina is sensitive to it, so many people observe this color shift following cataract surgery.

It’s not very sensitive to it, though, unless you’re a mutant, nor to violet either, so the effect is mostly in our perception of what we weren’t seeing at all, rather than a large amount of violet/ultraviolet getting through. During early dawn, though, the violet light is the only light getting scattered enough to see at all, so it dominates. To the rest of us, it just looks black, then very dark blue.

The diagram in the above linked to article - in the bit “why not violet” contains the answer, although the description isn’t totally clear on the critical point. Look at the diagram that shows the spetcral response of the eye. Notice the little hump on the left in the red sensitivity. That is why the sky isn’t violet.

The humam eye isn’t linear in its perception of colour with respect to wavelength, and worse, isn’t always even monotonic. Our naive expectation is that as the wavelength goes shorter and shorter it will be perceived as a continuous change of colour from red to blue. But the way the eye works is much messier, and that little hump in red sensitivity has the effect of causing the perceived colour to fold back on itself slightly.

They sky is more violet than we see it. The other answers about the relative intensity of light from the sun contribute too, but the eye’s own colour response is a big influence. Basically it isn’t violet because our eye has a sensitivity anomaly that renders that particular combination of wavelengths more blue than a simple colour mixing analysis would suggest it should.