Why is the sky blue? Rayleigh scattering. Everyone and their mother has done that video. Do you have any sevens? Go fish. But why isn’t everything blue? Why isn’t the sky purple? Fine, I’ll do the video. Do you have an tens? Go fish. This episode was made possible by generous supporters on Patreon. Hey Crazies. It’s real easy to be dismissive with an explanation that’s a century old. Especially when there are already this many videos about it. But, now that Question Clone has asked some deeper questions, I’ve got something to add. Let’s do this! As I mentioned earlier, the blue sky is caused by something called Rayleigh scattering. Named after John William Strutt, 3rd Baron Rayleigh. Otherwise known as Lord Rayleigh. "Rayleigh" is peerage of nobility named after a market town near where his family was from. He inherited it from his father, who inherited it from his mother. You know, nobility stuff. This doesn’t actually matter! The point is, he started thinking about this all the way back in 1871 and didn’t put it all together until 1899. Which is, what? Like, 120 years ago? We’ve known about this a long time, is what I’m saying. The explanation goes something like this. When direct light from the Sun enters the atmosphere, it begins to scatter around. However, this scattering is color dependent. Higher frequency visible light, that means light near the blue end of the visible spectrum, is scattered almost ten times as much as light near the red end of the spectrum. Which is great and all, but, like, why? Why does the color even matter? To answer this, we’re going to have to go a little deeper into how scattering actually works. I talked a little bit about scattering in this video, but that was for solid surfaces. The Earth’s atmosphere is a gas. Almost entirely nitrogen and oxygen gas to be specific. Something about these molecules must be important. As it turns out, both nitrogen and oxygen gas have strong resonances in ultraviolet. Resonances? Right, I guess I should explain that a little. Light, visible or otherwise, is an electromagnetic wave, a disturbance in the electromagnetic field. The energy from a wave like that can be absorbed by electric charges, like the ones you’d find inside atoms and molecules. When the light wave encounters a molecule, the charges inside it will start wiggling. We say the wiggling is being driven by the light. And this is a very classical effect. No quantum mechanics necessary. Newton’s second law is enough to describe it. The total force on something determines its acceleration. Wiggling is a type of acceleration. Since it’s the electron cloud doing most of that wiggling, this should be the mass of that cloud. As for the forces, that depends on how accurate we want to be. Lucky for us, even the simplest model will make my point. Two forces is enough. One force is the driving force from the light wave. It’s an electric force because light is an electromagnetic wave. The other force is called a restoring force. It comes from the bond that holds the electrons in the molecule. Resonances? Yes, yes, we’re getting there. Notice these two frequencies are different. The one in the driving force is the frequency of the light. The one in the restoring force is the resonance of the molecule. That’s the frequency the molecule naturally wants to wiggle at. The closer the frequency of light is to that resonance, the bigger the wiggle. Since color is directly related to frequency, the color matters. So, how do we get from absorbing to scattering? That wiggling creates its own light. As we said earlier, a wiggle or vibration is a type of acceleration, but accelerating charge emits light. That’s how light is made. Yes, for real. When the incoming light makes the molecule wiggle, that wiggle creates its own light. Except this 1-dimensional picture isn’t quite accurate. The truth is, we live in a 3-dimensional world and that new light goes out in almost all directions. It’s called dipole radiation and it’s very relevant to Rayleigh scattering. Let’s keep things as simple as possible and imagine sunlight as a bunch of parallel wave fronts. They represent the peaks in the electromagnetic wave. When they encounter an air molecule, that molecule will absorb some of the energy and emit its own light with wave fronts that look like this. It’s emitted in every direction except the wiggle axis. But don’t forget about the resonance. Because the molecule wiggles more when the frequency of light is near that resonance, more of that light is scattered. There’s a color preference. And, as we mentioned earlier, the resonances for nitrogen and oxygen are in the ultraviolet range. Since blue is closer to ultraviolet than red, blue light scatters more. Almost 10 times more! Except, that’s not the whole story. You’ve got to talk about wave interference. (frustrated exhale) You’re right, as usual. The truth is, Rayleigh scattering only happens in the upper atmosphere. It requires the molecules be very far apart and randomly placed. Down here in the lower atmosphere, near the surface of the Earth, the molecules are only about 3 nanometers apart, but the wavelengths of visible light are in the 100s of nanometers. That means we also need to worry about wave interference. If all these molecules are becoming their own little radiators and their spacing is only a 100th of the wavelength, then the chances of one molecule being half a wavelength away from another are extremely high. Two waves that are half a wavelength out of phase will interfere and cancel each other. It’s called destructive interference. This will happen most places throughout the air, leaving only the forward moving sunlight. Solids and liquids are even denser than that, Hundreds or even thousands of times denser. That’s why, in most substances, there’s only one path for the light: the refracted path. To stop this kind of interference, we need the density of the air to be extremely low. The molecules need to be separated by at least a whole wavelength for Rayleigh scattering to occur and not cancel itself. That only happens in the upper atmosphere. All the blue you see in this image is coming from up near space. The light only scatters around for a bit. As it reaches denser and denser air, its path straightens out. By then though, the blue is coming from all directions. Also, technically, the sky isn’t blue. It’s bluish white. While blue is being scattered more, all the colors are being scattered a little bit. All the colors together make white, but white dominated by blue is bluish white. This also explains why the Sun looks yellowish when it’s actually pure white. The direct light from the Sun is missing the blue because it got scattered away to the rest of the sky. Also, also, sunset and sunrise look yellow and orange for the same reason. The light travels through the upper atmosphere longer at that angle, which means more Rayleigh scattering. So much, in fact, that the blue is scattered away from your eyes completely. But why is the sky blue and not purple? Right, right, I almost forgot. Ok, one last thing before we finish up. You can see from the visible spectrum that there really isn’t much purple. Purple or violet is the color on the very very edge, right around 400 nanometers. It’s actually so close to the edge of the human visible range that some people can’t even see it. The purple colors that most people see are just combinations of red and blue, like this magenta color, rather than actual monochromatic purple. The sky is scattering ultraviolet light too, a lot more than visible light actually. The only reason the sky isn’t purple is because purple isn’t very visible. It’s there. We just can’t see it. So why is the sky blue? It’s blue because of Rayleigh scattering in the upper atmosphere. Sunlight drives the motion of electron clouds inside of air molecules. That wiggling generates its own light that goes out in almost all directions. Since these molecules resonate in ultraviolet, blue scatters far more than red. If the molecules are far enough apart, this new light will continue to scatter and ultimately arrive at your eyes from all directions, which makes the sky appear blue from all directions. And now, you know better. Wait, why did I just say that? Anyway! Did I go deep enough for you? Let us know in the comments. Thanks for liking and sharing this video. A special thanks goes out Fabio Manzini for being one of our new orderlies on Patreon. I can’t thank my Patreon patrons or channel members enough for all their help, but I try my best with perks like a monthly live Q&A. Pledging even one dollar per month gets you access. So, thanks to all my supporters for making this channel and, frankly, my life possible. Don’t forget to subscribe if you’d like to keep up with us. And until next time, remember, it’s ok to be a little crazy. To everyone in the last video going on about multilinear maps or hoping for a more math-oriented explanation of tensors, Tai-Danae, former host of PBS Infinite Series, has a blog post you should check out. Link in the doobly-doo. Anyway, thanks for watching! Wait! Question Clone stole my turn! That mother...
