Why is the sky blue? The physics of sunlight and air

The sky is blue because sunlight, which contains every color, is scattered by the molecules of the air, and the short blue wavelengths are scattered several times more strongly than the long red ones. That scattered blue light reaches your eyes from every part of the sky, so wherever you look away from the Sun, the air glows blue. The effect is called Rayleigh scattering, and it also explains why the sky isn't violet and why sunsets are red.

In short

• Air molecules are far smaller than a wavelength of light, and particles that small scatter short wavelengths much more than long ones.
• Violet is scattered even more than blue, but the Sun gives off less of it and human eyes are less sensitive to it, so the sky looks blue.
• At sunset, light crosses so much air that most blue is scattered away before it arrives, leaving reds and oranges.

What is sunlight made of?

Sunlight looks white, but it is a mix of all the colors of the rainbow, as a prism shows by spreading them apart. Each color is light of a different wavelength. Red light has the longest visible waves, around 700 nanometers (billionths of a meter) from crest to crest; blue is around 450 nm; violet, the shortest human eyes can see, around 400 nm. All of it travels at the speed of light, and together it reads as white. The light itself comes from the Sun's hot surface, as the note on what the Sun is made of explains.

On the way down to the ground, that light passes through about 100 km of atmosphere, mostly nitrogen and oxygen molecules. Each molecule is around a thousandth the size of a light wave. What happens when the light meets them gives the sky its color.

Why do air molecules scatter blue light most?

When a light wave passes a molecule, its electric field makes the molecule's electrons jiggle back and forth at the same frequency. A jiggling charge gives off light of its own in all directions. That re-sent light is scattered light: a small share of the sunlight is turned aside from its straight path and spread across the sky.

For particles much smaller than the wavelength, the strength of this scattering depends steeply on the wavelength: it goes as 1 divided by the wavelength to the fourth power. Lord Rayleigh worked out the mathematics in 1871, building on experiments by John Tyndall, which is why it is called Rayleigh scattering. The fourth power is what makes it so lopsided.

Working it out: how much more is blue scattered?

Compare blue light at 450 nm with red at 700 nm. The ratio of wavelengths is 700 ÷ 450 ≈ 1.56. Raise that to the fourth power: 1.56 × 1.56 × 1.56 × 1.56 ≈ 5.9. Blue light is scattered almost six times as strongly as red. For violet at 400 nm, the same sum gives (700 ÷ 400)⁴ ≈ 9.4, which matches the "about 10 times" that physicist Philip Gibbs gives in the Physics FAQ.

So when you look at a patch of sky away from the Sun, you are not seeing sunlight directly but light that has been bounced toward you by air molecules, and that light is heavily weighted toward the blue end. The light that comes straight through from the Sun looks slightly yellowish white, because some of its blue has been scattered out along the way.

If violet scatters more, why isn't the sky violet?

Three reasons combine. First, the Sun gives off less violet light than blue in the first place. Second, as the Physics FAQ notes, some violet is absorbed high in the atmosphere. Third, and most important, human eyes are much less sensitive to violet. As the U.S. National Weather Service puts it, the sky looks blue rather than violet because human eyes are more sensitive to blue light.

Your eyes see color with three kinds of cone cell, tuned roughly to red, green and blue. The mix of scattered light coming from the sky, which includes plenty of violet and blue with smaller amounts of green, yellow and red, stimulates them in a combination the brain reads as a pale sky blue. The sky's color is partly physics and partly the biology of the eye.

Why are sunsets red and orange?

At noon, sunlight takes a short route straight down through the atmosphere. Near sunrise and sunset, it comes in at a low angle and crosses a far longer path through the air, dozens of times longer than at noon when the Sun is at the horizon. Along that path, most of the blue and violet is scattered out sideways before the light reaches you. What is left in the direct beam is the long-wavelength end: yellow, orange and red. NASA's Space Place describes it the same way: even more of the blue light is scattered, allowing the reds and yellows to pass straight through.

Dust, smoke and pollution add to the effect. Particles from wildfires or volcanic eruptions can make sunsets especially deep red. These larger particles scatter by a different process, called Mie scattering, which treats all colors more evenly.

Why are clouds white and space black?

Clouds are made of water droplets, which are much larger than a wavelength of light. Particles that large scatter all visible colors about equally, so a cloud sends back white light. Thick storm clouds look gray because little light gets all the way through them.

Space is black because it has no air to scatter anything. On the Moon, which has almost no atmosphere, the sky is black even at midday, which is why photographs from the Apollo landings show a black sky above a sunlit surface. The blue sky is a property of Earth's air, not of sunlight itself, and other phenomena in the air, such as the northern lights, come from entirely different physics: atoms glowing after being hit by particles from the Sun.

What color is the sky on Mars?

Almost the reverse of Earth's. Mars has a thin atmosphere full of fine reddish dust, and the dust, not the gas, sets the color. By day, the Martian sky is a dusty orange or butterscotch, which NASA's Space Place calls an orange or reddish color. At sunset, the area around the Sun turns blue-gray.

NASA's Curiosity rover photographed one of those blue sunsets on 15 April 2015, the mission's 956th Martian day. According to NASA's Jet Propulsion Laboratory, the fine dust lets blue light penetrate the atmosphere more efficiently, and that blue stays close to the Sun's part of the sky while yellow and red scatter more widely. For more on the planet itself, see what Mars is like.

Is the sky blue because it reflects the ocean?

No. That is a common myth, and it has the story backward. The sky is just as blue over the Sahara and Antarctica as over the Pacific. The ocean looks blue partly because its surface reflects the blue sky and partly because water itself absorbs red light more than blue, so deep water has a faint blue color of its own. A gray, overcast sky turns the sea gray too. The test of an idea against cases like these, a desert sky or a cloudy day, is how science separates an explanation from a guess.

Check yourself

• Without looking back: why does the size of air molecules, compared with a wavelength of light, matter for the color of the sky?
• Violet light is scattered more than blue. Give the reasons the sky still looks blue.
• Explain why the same scattering that makes the noon sky blue makes the sunset red.

Sources

• Why Is the Sky Blue? — NASA Space Place
• Why is the sky blue? — U.S. National Weather Service, Flagstaff office
• Why is the sky blue?, Physics FAQ — Philip Gibbs, 1997
• Sunset in Mars' Gale Crater — NASA Jet Propulsion Laboratory, 8 May 2015
• Rayleigh scattering — Wikipedia