Okay, let's to an #OpticsLessonOfTheDay: why is the sky blue? The answer is an interesting mix of several different aspect of physics as well as the working of the human eye.
First off: we note that the sun radiates light somewhat uniformly over the entire visible spectrum of light, which ranges from 380 to 750 nanometers. (Image via Wikipedia.) It peaks a bit in the middle of the spectrum, so we picture the sun as a bit more yellow than white. 
Now, during the day, we see blue light everywhere *except* in the direction of the sun. This is because the gases in the atmosphere preferentially scatter blue light. All the blue you see is from light scattering off of atmospheric molecules.
(Image taken from the NOAA website: scijinks.gov/blue-sky/ )
Okay, need to take a break for lunch.
Individual small particles scatter shorter wavelengths much stronger than long wavelengths, in a phenomenon known as Rayleigh scattering. The actual law is the strength of scattering goes as 1/wavelength to the fourth power…
This means blue light scatters much more strongly than red light. Red is on the long end of the visible wavelength spectrum, while blue is near the short end of the spectrum. Thus we see blue light scattered by the sky!
Also, at sunset, the sun appears red because the sunlight is traveling over a longer path through the atmosphere- all the direct blue light gets scattered away, leaving us red! (Albert Biersstadt, Island of New Providence, 1891)
But wait - violet light has an even shorter wavelength than blue! Why isn’t the sky violet? (Image via Wikipedia)
There are two reasons. First: look at the solar spectrum again. It drops off in intensity at the violet end of the spectrum. Thus, even though violet light gets scattered more than blue, there’s simply less of it coming from the sun to begin with.
The other reason is that our eyes simply are not as sensitive to violet at the far end of the spectrum. Thus, due to there being less violet light and less sensitivity to it, we tend to see a blue sky.
“Not as sensitive” is a way for me to gloss over how our eyes actually detect color, which is a whole can of worms I don’t wanna open right now.
Okay, eating - more soon.
Let's go a little deeper into this explanation -- *why* is blue light scattered more than red light by small particles in the atmosphere? Here, we're going to try to talk very generally and profoundly about wave optics.
First of all: the scattering of light by a particle is a pure wave phenomenon. It involves a wave coming in from a single direction, interacting with the particle, and scattering into a wide range of directions.
As a wave, light has a wavelength associated with it: the distance between peaks of the wave. Again, blue light is around 450 nanometers in wavelength, much shorter than red, which is around 650 nanometers in wavelength. britannica.com/science/light
When do the wave properties of light become important, i.e. when does light start acting more like a wave than a particle? Well, you can imagine the wavelength acting like a yardstick by which an individual light particle (photon) measures everything it interacts with.
If a photon interacts with something much bigger than itself, i.e. the object is bigger than the wavelength, then the wave features of light don't play a significant effect.
We see this in diffraction theory: when light goes through a hole much bigger than the wavelength, you can really describe the interaction using a geometric picture of light. When the hole is comparable or smaller than the wavelength, then diffraction effects become stronger.
If light is interacting with an object or particle much smaller than the wavelength, then there is also typically a very weak interaction. The "big" photon doesn't "see" the "small" particle.
This brings us back to Rayleigh scattering which is the model used to describe light scattering by small particles. The particles are treated as being *much* smaller than the wavelength of light.
However, a smaller wavelength will "see" this small particle more than a particle with a larger wavelength will. Roughly speaking, this is why short wavelengths scatter more strongly than long wavelengths.
This is a *very* rough description, but if you think of the wavelength as a "ruler" for light, it helps you understand a lot of wave phenomena on a lot of different scales. For instance, visible light reflects off of a mirror, but x-rays scatter: why?
Because the wavelength of x-rays is so short it is comparable to the size of the individual atoms making up the mirror itself! Whereas visible light "sees" a smooth surface, x-rays see the roughness of the surface on the atomic level.
Historical note: this inability to make x-rays reflect at a smooth surface presented a challenge in the early 1900s to prove that x-rays are a form of electromagnetic wave! skullsinthestars.com/2009/06/06/bar…
Incidentally, even the picture of light scattering by small particles in the atmosphere is a bit too simple! As is discussed in a number of books on random media, the real scattering effect isn't due to single particles, but fluctuations of the atmosphere.
In other words, the atmosphere can be viewed as a continuous medium with a density that fluctuates in space and time; sunlight is scattering off of small pockets of these fluctuations, which produces the same 1/wavelength^4 dependence on scattering.
(I doublechecked this in a classic text by Ishimaru on wave scattering by random media.)
Let's talk about one more curious effect associated with atmospheric scattering: polarization! I've talked many times how light is a transverse electromagnetic wave, which means the electric and magnetic fields wiggle perpendicularly to the direction the wave is going.
Light coming from the sun is unpolarized: it is a random mixture of "up-down" wiggles and "left-right" wiggles. If you point a polarizer right at the sun (note: do not look right at the sun, polarizer or no), you will see that rotating the polarizer doesn't change brightness.
But when light scatters in the atmosphere, it can only scatter in a direction that allows it to remain transverse. Light can't scatter in a direction parallel to the direction of the incident light's wiggles. This means that the blue sky is partially polarized everywhere!
You can see this by looking through a polarizer (or polarized sunglasses) at the sky and rotating it. Here's an old video I did of the effect:
There's probably even more to say, but I'll stop here! Hope this illuminates why the sky is blue! /END
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