A child asks: “Why is the sky blue?”

What are you supposed to say? You don’t know the answer. The technical answer is Rayleigh scattering, but that seems like the sort of thing you learn about in a graduate class on electromagnetism.

I hope to give you an answer that you could explain to a child.

After writing this, I found that NASA has written something similar here. I like my version better, although I might be biased.

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Prerequisites: None.

Originally written: June 2019.

Confidence Level: Established science since the late 1800s.

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The Sky without the Atmosphere

Two things contribute to the color of the sky: the sun and the atmosphere.

We know what the sky looks like without the sun because we see it at night. The sky is black. The only light we see is the light from other stars and the light from the sun that’s been reflected from the moon or from other planets. If we are unfortunate (and most of us are), we also see light from nearby cities, which washes out the beauty of the stars.

What would the sky look like without the atmosphere?

Once again, the sky would be black. When we look up, we could be looking directly at the sun, a planet, or a distant star. If we aren’t, then there is no source of light between us and the edge of the observable universe. Without a source of light, the sky appears black.

This was most dramatically seen by the Apollo astronauts on the surface of the moon. Without an atmosphere, the sun is brilliant. The landscape is completely illuminated, except for the sharp shadows caused by the topography. But the sky remains black. Whenever I hear the phrase,

The light shineth in the darkness; and the darkness comprehended it not,

John 1:5

I think of walking on the moon.

If either the sun or the atmosphere were gone, the sky would be black. The blue color of the sky must be the result of sunlight interacting with the atmosphere. If there is less atmosphere above us because we are at higher elevation than usual, the sky is a darker blue. If there is more atmosphere above us because the atmosphere also contains a bunch of water or smoke today, the sky is a lighter blue – unless there is so much that the light from the sun has a hard time reaching us at all and the sky is gray.

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Resonance

It is hard to affect something that is a thousand times larger than you. It is also hard to affect something that is a thousand times smaller than you.

It is hard to affect something that moves a thousand times more quickly than you. It is also hard to affect something that moves a thousand times more slowly than you.

Interactions are typically the strongest when the objects interacting are closer to the same size or move at close to the same rate. If you want to move something, don’t start with either a mountain or a speck of dust. If you want to move a swing, your motion should match the frequency with which the swing moves on its own.

This is the key idea of resonance.

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Sizes

Air consists of a bunch of molecules. Air has a low density. The molecules are far enough apart that they don’t interact with each other very much. When light interacts with air, it is interacting with each individual molecule separately.

What is the size of the molecules in the air?

The most common molecules in the air are nitrogen ($N_2$) and oxygen ($O_2$), both of which consist of two atoms. Other common molecules consist of a single atom such as Argon ($Ar$) or three atoms such as Carbon Dioxide ($CO_2$) or water ($H_2O$). Atoms are about one angstrom, or one ten billionth of a meter. The size of the molecules in the air is a few times larger.

What is the size of visible light?

This is a weirder question because it is not immediately obvious that light has a size. The size of light corresponds to its wavelength. The wavelength of visible light is several hundred nanometers. A nanometer is one billionth of a meter or ten angstroms.

The wavelength of visible light is about a thousand times larger than the molecules in the air, so there is no resonance. There is very little interaction between light and air.

This explains why air is transparent.

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Colors

The atmosphere contains a lot of air and the sun is very bright. Even though there is not much interaction between the air molecules and the sun, there is so much light and air that we can still see a significant effect.

What light is most likely to interact with the molecules in the air?

The light with the smallest wavelength, blue light, is the closest to resonance. It’s still hundreds of times bigger than the molecules in the air, so the air is still transparent to blue light, but the wavelength is closer to the size of an air molecule than the wavelength of red light.

Wait. Blue isn’t the smallest wavelength of visible light. Purple is.

Why isn’t the sky purple?

Just because the molecules in the air are mostly likely to interact with purple light doesn’t mean that they don’t interact with the other colors of light at all. There is a small amount of interaction between purple light and air, a smaller amount of interaction between blue light and air, a tiny amount of interaction between green light and air, an even tinier amount of interaction between yellow light and air, and almost no interaction at all with red and orange. So when we look at the sky, we don’t see only purple light. We see small purple + smaller blue + tiny green + tinier yellow.Your eye merges these colors together and ends up with a light shade of blue.

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Sunrise and Sunset

If you look directly at the sun during the day, you see light.^[1]Citation Needed. The light looks white and then doesn’t look like anything because your eyes stop working. White light is a mixture of all colors. Sunlight from overhead hasn’t traveled through enough atmosphere to noticeably change its color.

What if you look at the sky in a different direction? The light that reaches your eyes was originally going to hit somewhere else, but bounced off an air molecule and went to your eyes instead. Because it had to interact with the air, this light is blue.

Since we removed some blue from that light, wouldn’t that change its color? Yes, but only a little bit. Not much blue light was removed. The sky is not nearly as bright as the sun. But the light that is left is slightly tinted away from blue and is maybe a light yellow.

At sunrise or sunset, light from the sun has to pass through much more atmosphere. The atmosphere is about $100 km$ ($62 mi$) thick,^[2]Unlike in these figures, the atmosphere doesn’t have a top. The air just gradually gets thinner and thinner. There are several different definitions, but the most common one is Kármán line at … Continue reading but when the sun is just above the horizon, its light has to pass through $1500 km$ ($930 mi$) of air.

Although $100 km$ ($62 mi$) of air only removed a negligible amount of blue light from the air, $1500 km$ ($930 mi$) of air removes much more. What’s left is red and orange. This is why the sun looks red at sunset. The sun is still producing the same white light that it always produces, but only the red light can make it through the atmosphere to our eyes.

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Mars

Mars has a much thinner atmosphere than Earth. There is not enough air for sunlight to bounce off of to make the sky blue.

Mars has a lot of dust. Most of the dust on Earth gets wet and sticks together. Since Mars doesn’t have lots of liquid water, the dust there stays dust.

Mars’s thin atmosphere is enough to blow dust around. There is always some dust in the air. Sometimes, giant dust storms arise that can block out the sun for weeks. This dust is the same color as Mars is – red.

When you look at the Martian sky, you don’t see blue light bouncing off of air molecules, you see red light bouncing Martian dust.

During the day, the sunlight hasn’t traveled through enough dust to change its color (unless there is a dust storm). At sunrise or sunset, sunlight has to travel through a lot more dust. On Earth, the blue light bounces off the air, leaving redder light behind. On Mars, this is reversed. Red light bounces off the dust, leaving blue light behind. Sunsets on Mars are blue.

This pattern is easy to generalize. Whatever color the sky is during the day, the sun must be the opposite color during sunset. The sky is the color of light that interacts with the atmosphere. The sunset is the color of light that is left behind.

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Lunar Eclipse

A lunar eclipse occurs when the moon passes through the shadow of the Earth. When the shadow is only partially covering the moon, it looks exactly how you would expect. Part of the moon is dark, but the shape isn’t a normal crescent or gibbous and changes much more quickly than the phases of the moon (hours instead of weeks). When the moon is entirely in the Earth’s shadow, it becomes much fainter. But, surprisingly, it isn’t completely dark.^[3]During a solar eclipse, when the Earth is in the moon’s shadow, the moon appears as a black disk in the sky, surrounded by the sun’s atmosphere. We don’t see anything like a blood … Continue reading Instead, this “blood moon” shines a dark red. Why?

Normally, the light we see from the moon goes from the sun to the moon, then bounces off the moon and comes to the earth. During a lunar eclipse, light can’t come directly from the sun to the moon because the Earth gets in the way.

Earth’s atmosphere can act like a lens. Just like glass (transparent, but denser than air) can bend the path of light traveling through air, air (transparent, but denser than space) can bend the path of light traveling through space. Only the light that just barely skims the surface of Earth can be bent this way. If the light is farther from the Earth, there is no atmosphere. If the light is closer to the center of the Earth, it will hit the ground and not make it to the moon. Only a little light successfully travels this path, so the moon during a lunar eclipse is much less bright than normal.

All of the light that reaches the moon during a lunar eclipse has to go through the Earth’s atmosphere first. Most of the blue light is bounces off air molecules in the atmosphere, so only the red light remains. This red light then illuminates the moon. The moon reflects some of the red light back to Earth. We see the moon as a dark red color.

The light that reaches the moon during a lunar eclipse has to just barely skim the Earth, so it has to travel close to the boundary between day and night. We have special names for this boundary: sunrise and sunset. The blood moon is even redder than sunrises and sunsets because the distance that light travels through the atmosphere is twice the distance shown in Figure 4. Any light that reaches the moon has to travel through a sunrise or sunset somewhere on Earth.

A blood moon glows with the light of all of the sunrises and sunsets on Earth.