The Sky is the Daily Bread of the Eyes
~Ralph Waldo Emerson

 

At some point in his or her life, almost every child on Earth asks, “Why is the sky blue?” The question is so prevalent that, to me, it has come to represent the wonder that the world holds for a a child. Adults don’t ask such questions… at least, not unless they’re scientists.

Part 1: John Tyndall

In 1859, physicist John Tyndall thought he’d found the answer to the sky’s color. His studies of infrared radiation required him to use containers of completely pure air. He discovered an ingenious way to detect whether or not his air was sufficiently pure: shine intense light through it. The light would scatter off of any dust motes or other particles, causing telltale “sparkles” that let Tyndall know he wasn’t finished purifying the air.

But Tyndall also noticed something strange. When light did scatter, it was disproportionately blue-tinted–but light that passed through the air without scattering was disproportionately red-tinted. We can see this effect in the figure below, which shows clear light passing through opalescent glass. The glass itself lights up blue, but the light that comes out the front is orange. This is called the Tyndall effect, or Tyndall scattering.

(If you want to see this effect for yourself, pour just a tiny bit of soap or milk into a glass of water and shine a small flashlight through it. The path of the light through the water will be visibly blue. There are also several videos on Youtube.)

In a staggering leap of logic, Tyndall extrapolated from his dust-particle experiments to the color of the sky. Perhaps, he thought, the scattering of sunlight off of particles in the air causes that familiar blue tint! By Tyndall’s time, physicists knew that white light is a wave made up of all the colors of the visible spectrum, and that one can separate the colors of light using a prism.

Tyndall’s basic idea is shown below. As (roughly) white sunlight enters the atmosphere, the blue light scatters off of dust particles in the air and spreads throughout the sky. Eventually some of it scatters down to our eyes and makes the sky appear blue. The remaining, non-scattered light is yellow or orange, and this is what we perceive as the light coming directly from the sun.

Incidentally, Tyndall’s theory also explains why sunsets are red. When the sun is parallel to the Earth, none of the Tyndall-scattered blue light reaches our eyes at all–we see only the red light left over after the rest has been scattered.

Not all the technical details of this theory are correct. It turns out that sunlight is not pure white light, but closer to a blackbody spectrum. The particles that the sunlight scatters off of are not dust particles, but rather pockets of hotter or cooler air, which act like particles due to refraction. And the fact that we see the sky as blue, rather than violet (an even shorter wavelength of light that experiences even more scattering), has more to do with how the human eye evolved than anything special about blue light itself. Nevertheless, Tyndall’s idea is essentially right–and a brilliant logical leap after a happy accident of discovery.

Part 2: Lord Rayleigh

But why does blue light scatter more than red light? And, for that matter, how does scattering work at all? If light is a wave, it can’t just bounce off of a particle, can it? (Of course, light is both a particle and a wave, but the description is still deeper than “bouncing.” We’ll talk about that in a bit.)

In 1904, John William Strutt, better known as Lord Rayleigh, examined the Tyndall effect more carefully. In the time since Tyndall, James Clerk Maxwell had discovered that light is made of electric and magnetic fields. (For a more detailed description, see my article on refraction.)

Maxwell discovered that these fields can feed into each other and become self-sustaining. A changing electric field produces a magnetic field, which produces an electric field when it changes, and so on. Moreover, when these fields oscillate like this, they behave exactly like light–meaning that light is a wave made up from these fields! (I am, of course, glossing over the fact that light is both a particle and a wave. From the quantum perspective, the electromagnetic wave describes the probability of detecting a photon at a given place and time.)

Rayleigh also knew that an atom is made up of a positively-charged nucleus surrounded by negatively-charged electrons. (As we know from Bohr, this is essentially correct.) What would happen if you were to somehow pull one of these electrons away from the nucleus? Assuming you didn’t pull too hard before you let go, the nucleus would pull the electron back in, and the electron would oscillate around the nucleus like a mass on a spring.

Of course, the electron was already (to a good approximation) orbiting in a circle around the nucleus, and it doesn’t stop orbiting after we perturb it. But because it keeps overcorrecting for the perturbation, the electron yo-yos back and forth between two elliptical orbits.

Rayleigh’s insight was that a propagating electromagnetic field–that is to say, light–pushes and pulls at the electron in the exact way necessary to make it wobble back and forth. Of course, there’s a price to pay. Wobbling the electron costs energy, which is taken out of the electromagnetic field, causing the incoming light to be absorbed by the atom and disappear.

But the electron doesn’t stop wobbling after the light is absorbed! The electron’s motion keeps tracing out the shape of the light’s electric field. And since the electron is a charged particle, this tracing-out actually recreates its electric field–producing more light of the same color as the original! To reiterate: The electron absorbs the original light, then re-emits it in a random direction. We call this behavior Rayleigh scattering.

So why is the scattered light more likely to be blue? Well, electrons interact better with light when they’re accelerating very quickly. And because blue light has a shorter wavelength than red light, it accelerates the electrons more quickly, which makes them more likely to absorb light. (I know this isn’t a terribly satisfying answer…but you’ll have to trust me when I say that it emerges in the mathematics.)

As always, I’m glossing over many, many details here. Rayleigh’s calculation only works for very small particles, which the particles in the sky are not. And it’s important that the electron doesn’t wobble at a specific frequency…otherwise, a phenomenon called resonance makes electrons absorb a much larger fraction of incoming light. (I will explain resonance sometime in the future, I promise!) And, of course, the completely correct picture is quantum mechanical in nature, but I’m going to save that for next week’s post.

Part 3: Adolf Smekal and Sir C.V. Raman

Rayleigh gave us an explanation for how light scatters off of atoms. But what about molecules? As it turns out, things don’t work the same way at all! In 1923, the unfortunately named Adolf Smekal predicted that, if light scatters off of a molecule, some of the scattered light should be a different color than the incoming (or “incident”) light. And in 1928, the brilliant experimentalist Sir Chandrasekhara Venkata Raman verified the effect. His discovery won him the Nobel prize.

In an atom, electrons are localized to one nucleus. But in a molecule, the electrons have several atoms to roam across. (As I discussed in my post on bonding, atoms in a molecule share electrons.) When an electromagnetic field comes along, it pushes the electrons into preferred positions, which causes the molecule to polarize–meaning that certain parts of the molecule are positively charged and other parts are negatively charged.

So far, this isn’t too different from electrons in single atoms. After all, our electromagnetic field moved the electron then, too. But atomic bonds in molecules are not static things. Because of the heat in the molecule, the atomic bonds wobble and vibrate all on their own. This means that once a molecule is polarized, the electrons wobble, too!

So what happens to incident light? Well, the wiggles of the electromagnetic field do indeed wiggle the electrons. But the electrons’ wiggling speed is affected by how much the molecule itself is wiggling. Thus, the wiggle that the electrons trace out to produce the new outgoing light is different than the wiggling of the incoming light alone. As a result, the scattered light can be a different color–either a higher or a lower frequency–than the original light.

(Again, there is a quantum mechanical explanation for all this, but we’ll skip it for now.)

Applications for Raman Scattering

Since the wobbling of the electrons in a molecule depends strongly on the type of atomic bonds within the molecule, Raman scattering can be used as an extremely sensitive probe of a molecule’s structure. The Raman spectrum of a molecule can even act as its identifying “fingerprint.” This is especially helpful in organic chemistry, which gives typical spectroscopy methods trouble, because organic molecules are overwhelmingly composed of the same handful of elements–carbon, hydrogen, and oxygen–but can take on incredibly complicated shapes. For example, the figures below show the Raman spectra of hexane, a relatively short string of carbon atoms with hydrogen “fingers,” and graphene, a two-dimensional honeycomb lattice of carbon atoms. (Graphene is amazing stuff, by the way…amazing enough that you should expect a whole post on it at some point.)

(A small brag: these Raman spectra plots are actual data taken by me when I was an undergraduate student. The measured graphene was even grown by me in the lab.)

 

If the atomic bonds change, the Raman spectrum can track that, too. (A lot of my undergraduate research involved measuring how the Raman spectrum of graphene changed when I poured acid on it.) All of this is very cool and interesting stuff…but I think I’ve written enough for now. 🙂

Further Reading

• You may find my post on refraction helpful.
• Optics and Photonics has a short biography of C. V. Raman
• They did one on Rayleigh too.
• Raman’s Nobel prize biography.
• Lord Rayleigh won the Nobel prize for his discovery of Argon gas. So he has a Nobel biography too.
• There are several free biographies of John Tyndall. You can find one of them on wikisource.
• John Baez has a short explanation for why the sky is blue.
• NASA has an explanation too.
• So does Science Made Simple.
• And How Stuff Works.
• And Minute Physics.
• And to be contrary, Veritasium explains why the sky is not blue.
• For the brave, here is a mathematical treatment of Rayleigh scattering.

Questions? Comments? Insults?

As always, if you have any questions, comments or corrections–or if you just want to say hi–please drop me a line.