初心 shoshin

Phantom in the Light

The story of early spectroscopy

I have set my rainbow in the clouds, and it will be the sign of the covenant between me and the earth.

Genesis 9:13

For much of human history, the rainbow was a supernatural phenomenon. In Judaic religions, it was a sign of God's covenant that he would never kill everyone on earth via a giant flood again.1 In Norse mythology, there was the Bifröst, the rainbow bridge that connected Midgard (the realm of man) to Asgard (the realm of the gods). Iris, in Greek mythology, was the goddess of the rainbow and divine messenger of the gods. For much of human history, the rainbow was as inscrutable as it was inconstructible.23

The Norse god, Heimdallr, lived at a place called Himinbjörg, where the Bifröst, the burning rainbow bridge, meets the realm of the gods. Heimdallr has keen senses of sight and hearing and keeps a perpetual watch for Ragnarök. This painting depicts Heimdallr sounding his horn at the end of times, Ragnarök.

Heimdallr, watchman of the gods, sounds the mighty Gjallarhorn, ending his perpetual vigil from Himinbjörg, where the Bifröst meets Asgard, the realm of the gods, and forewarning the world that the end of times, Ragnarök, is finally upon us. The Bifröst will soon shatter and the earth flood as Gjallarhorn echoes throughout the nine realms. Heimdallr's vigil ends not because he fails but because the time for Ragnarök has arrived, and his duty has been fulfilled. Okay, this image caption is a little long and detracting from the story I'm trying to tell, but what can I say? I like Norse mythology!

Isaac Newton

In 1672, Newton used a prism to divide white light. With this simple experiment, the prevailing Aristotelian dogma of the last 2000 years regarding light was overturned literally in a flash. Until white light came under the scrutiny of Newton's genius, it was thought that white light was pure, that it obtained color through interaction with darkness and matter. Newton showed that it was the other way around. White light is actually a combination of all other colors. Newton nailed the coffin shut on Aristotle's theory of light when he recombined a rainbow back into white light, showing once and for all that white light is indeed a combination.

Newton published the results of his experiments in his book4 Opticks in 1704. 5 In Opticks, he coins the term, "spectrum" (from Latin for "image" or "apparition"), to describe the range of refracted light, which is where we get the modern term, "electromagnetic spectrum."

Likely due to the crudeness of 1670s equipment, Newton did not notice that his spectrum was not actually continuous. There were tiny gaps in his refracted light. These gaps would go unnoticed for another 130 years. But what exactly were these gaps?

Fraunhofer Lines

The gaps in the sun's spectrum were finally noticed in 1802 by an Englishman, William Hyde Wollaston. Wollaston had invented a much-improved spectroscope using lenses that allowed him to view the same spectrum as Newton but in much greater fidelity. But Wollaston didn't know what the gaps were. He assumed they were the "gaps between colors" and left it at that.

Ten years later, the German physicist Joseph von Fraunhofer invented yet another improved spectroscope. Fraunhofer's spectroscope used a diffraction grating in place of a prism 6. A diffraction grating is just thousands of slits placed very close together. This permits two key things over prism-based refraction:

  1. The spectral resolution is even higher than with Wollaston's prism/lens combo.
  2. A diffraction grating allows the wavelengths of diffracted light to be measured.
A diffraction grating works by passing light through a series of tiny slits, rather than bending a single beam of light as a prism does via refraction. A diffraction grating provides two important improvements over prism-based diffraction—increased resolution and the ability to measure the wavelengths of the refracted light. This is a visual demonstration of these improvements.

1: Diffraction via diffraction grating. 2: Refraction via prism. Source.

Fraunhofer had never heard of Wollaston's discovery of the gaps in refracted solar light. But in 1814, he incidentally made the same observations. However, unlike Wollaston, Fraunhofer, with his new spectrometer, had the means to actually quantify these gaps. So he set out on a systematic analysis of the gaps in the solar spectrum. He identified 570 distinct lines giving each a unique label. 11 These gaps are now called Fraunhofer lines in his honor, but also referred to as "spectral lines."

With Fraunhofer's spectral measurements, the field of quantitative spectroscopy was born.

Range of visible light with various, seemingly randomly dispersed dark lines indicating Fraunhofer lines

Fraunhofer lines in solar spectrum

Bunsen, Kirchhoff, and the Three Laws of Spectroscopy

Different elements give off specific colors when heated. For example, sodium emits yellow light 12, potassium emits violet light, and strontium emits red light. This is known as the element's emission spectrum. An element's emission spectrum consists of a few bands of light emitted at particular wavelengths.

Notice that this is the opposite of what we were talking about in the previous section. Fraunhofer lines belong to an element's absorption spectrum. An absorption spectrum shows the full visible light spectrum, with particular wavelengths missing, rather than emitted. An element's emission spectrum, on the other hand, is just a few wavelengths (i.e., colors) of light.

The wavelengths that an element emits when heated correspond exactly to the wavelengths that are missing in its absorption spectrum. In other words, they are (almost 13) reciprocal. This is because they both result from the same electron energy transitions—absorption occurs when electrons jump to higher energy levels, emission when they fall back down. It didn't take scientists long to prove this (34 years to be exact 14).

The great thing about absorption spectra is that it makes identifying elements much easier. Just light something on fire and examine the light that's emitted. This discovery was a boon for experimental spectroscopy and led the advancement of not only chemistry but, as we'll soon see, astronomy as well.

Robert Bunsen and Gustav Kirchhoff were the main pioneers in flame spectroscopy (heating elements to examine their emission spectra). Bunsen is a name you've probably mostly heard preceding the word, "burner". Bunsen's eponymous device was designed specifically for the laboratory to maximize heat and minimize luminosity. Remember trying to get the perfect blue flame in chemistry lab? What a dopamine rush when you finally got it! This blue flame is not only the Bunsen burner's peak temperature, it's also nearly colorless at the top! This allows a chemist to burn an element and examine its color with minimal interference from the flame itself.

Burner in hand, Bunsen and Kirchhoff began their systematic analysis of burning a bunch of shit and examining the emitted spectra, publishing their results in 1860. 15 In the process, they discovered two new elements—cesium and rubidium, both of which were named for their emission spectrum. Cesium is Latin for "sky blue", and rubidium is Latin for "deep red".

Kirchhoff, in his three laws of spectroscopy, showed how black body radiation, absorption spectra, and emission spectra relate to one another:

  1. An incandescent solid, liquid, or gas under high pressure emits a continuous spectrum (that is, containing all wavelengths of visible light without interruptions).
  2. A hot, low-density gas generates an emission spectrum of bright lines corresponding to discrete wavelengths of light unique to the gas.
  3. A continuous spectrum viewed through a cooler, low-density gas produces an absorption spectrum, where specific wavelengths are absorbed, creating dark lines in the spectrum.
Visual depiction of the three laws of spectroscopy.  There are three graphs.  The first shows a continuous spectrum.  The second shows a mostly empty spectrum with a few lines.  The third shows a mostly full spectrum with a few lines missing.

Visual depiction of Kirchhoff's three laws of spectroscopy

Now, those Fraunhofer lines we talked about earlier are starting to make sense! Basically, the sun acts as a source of an enormous amount of black body radiation. That means the core of the sun is generating a continuous spectrum of visible (and non-visible) light (Law 1). But the sun gets cooler and less dense the farther from the center you are. Surrounding the core of the sun 16, is a layer called the photosphere. The photosphere is composed mostly (~98%) of hydrogen and helium gas trapped by the sun's gravity. The continuous spectrum emitted from the sun's core is "filtered" through the photosphere (Law 3). This creates an absorption spectrum where the Fraunhofer lines correspond to hydrogen, helium, sodium, and other trace elements found in the sun's atmosphere.

Twinkle, Twinkle Little Star

Twinkle, twinkle, little star,
How I wonder what you are!

From Jane Taylor's poem, "The Star" published in Rhymes for the Nursery in 1806

Have you ever thought about the first two lines to "Twinkle, Twinkle, Little Star"? When TTLS was written in 1806, people really didn't know what a star was. They might have guessed that they were "distant suns", but that hadn't been demonstrated in a rigorous scientific manner. The general public was even less clear as to what stars were.

The image of an 1888 woodcut titled the Flammarion Engraving depicts a man, dressed as a pilgrim in a long robe and carrying a walking stick, who has reached a point where the flat Earth meets the firmament. The pilgrim kneels down and passes his head, shoulders, right arm, and the top of the walking stick through an opening in the firmament, which is depicted as covered on the inside by the stars, Sun, and Moon. Behind the sky, the pilgrim finds a marvelous realm of circling clouds, fires and suns. One of the elements of the cosmic machinery resembles traditional pictorial representations of the 'wheel in the middle of a wheel' described in the visions of the Hebrew prophet Ezekiel.

This 1888 woodcut, the Flammarion Engraving, depicts a man reaching into space from "the edge of earth". Note the stars.

Spectroscopy is how we finally learned what stars really are. Scientists applied the same spectroscopic analyses they used on the sun to the stars 17, et voilà, we had an answer to Jane Taylor's poem.

The element, technetium (meaning "artificial" in Greek), for example, had only ever been artificially produced on earth. But in 1952, astronomer Paul W. Merrill detected technetium's spectral signature in the light from a class of stars called S-type red giants. Merrill's observation provided key evidence for the theory that many elements 18 are produced in stars via "stellar alchemy". This is because the most stable isotope of technetium is technetium-97, which has a half-life of 4.21 million years. This might sound like a long time, but from a star's perspective, it's the blink of an eye. 4.21 million years is far too short a time for technetium to have been present during the star's formation, meaning the star, itself, must be producing technetium (see Technetium star).

Technetium is not the only element forged in stars. Nearly every known element except for hydrogen (which was produced during the big bang) and the transuranic elements (too unstable) was at some time made in a star. 19 In other words, 90% of your body mass came from a star at some point! The other 10% of you (hydrogen) is about 13.8 billion years old, formed during the big bang. Carl Sagan worded it best:

We are star-stuff, the ash of stellar alchemy.

Carl Sagan, Cosmos

In just 150 years, humanity went from not having a clear idea of what stars were to being able to determine, through spectroscopy, their exact composition. And from their composition we can determine their lifecycle and the processes taking place inside them.

Conclusion

The inspiration for this story came from Isaac Asimov's book, Isaac Asimov's Guide to Earth and Space (1991). This is an embellished account of the same story he told there (with a few minor corrections 20).

It's fascinating how knowledge evolves over time and how we can use science to shape our understanding of the universe. With a few simple experiments on light, we can show that we are made from stars. I think the true nature of reality lies well beyond human imaginative capability, but science (and math and technology) allow us to peer just a little further into the darkness.

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Footnotes


  1. Though he said nothing about killing everyone on earth via other means! ↩︎

  2. The Romans were aware of the fact that rainbows could be constructed via prisms. But they neglected to ask how or why. As they were sometimes wont to do. See footnote 3↩︎

  3. The Romans were in some ways antithetical to the Greeks. The Greeks eschewed experimentation for theory, while the Romans eschewed theory for experimentation. Experimentation requires manual labor, and the Greeks, a slave-based society, equated this with slave labor. The Romans, on the other hand, were engineers and concerned with practical, rather than theoretical matters. Think roads, aqueducts, architecture, and military. The marriage of theory and experiment, via the scientific method, would have to wait until 1620 when Francis Bacon published his treatise, Novum Organum ("The New Instrument"). ↩︎

  4. Opticks was actually 3 books with a planned-but-never-written fourth book. ↩︎

  5. Observant readers will note that Newton published Opticks over 30 years after his experiments. Why did he wait so long to publish? In short, because Robert Hooke had just died the year prior. Newton presented his findings to London's Royal Society scientists as he made them. Robert Hooke, another prominent member of the Royal Society, took issue with Newton's proposed corpuscular theory of light. Newton didn't care for fame and cared even less for fighting. Instead of publishing and risking a public debate with Hooke, he waited until Hooke was out of the picture. ↩︎

  6. Fraunhofer originally used a prism and a slit to resolve the solar spectrum. While a narrow slit is not a diffraction grating in the modern sense, it acts as a spatial filter that sharpens spectral features when used with a prism. Around 1820, Fraunhofer developed and used veritable diffraction gratings—regular arrays of fine lines ruled on glass—which allowed for even higher precision in measuring spectral lines. ↩︎

  7. \(v = \frac{c}{n}\), where \(v\) is the speed of light in the medium, \(c\) is the speed of light in a vacuum, and \(n\) is the refractive index of the material. Note: this is the classical formula, and does not take into account dispersion. ↩︎

  8. Shorter wavelengths refract more than longer wavelengths. As light travels through a medium, its electromagnetic field interacts with the electrons of the medium’s atoms, and the shorter the wavelength the stronger oscillations in the medium’s electrons, leading to greater changes in speed and direction. See footnote 8↩︎

  9. This is the same process that is involved in ionizing and non-ionizing radiation. The energy, \(E\), in electromagnetic radiation (EMR) is inversely proportional to wavelength, \( \lambda \). Here's the equation: \(E = h f = \frac{hc}{\lambda}\), where \(h\) is Planck's constant and \(c\) is the speed of light in a vacuum. EMR with a sufficiently short wavelength, has enough energy to completely remove electrons from atoms (i.e., ionize them). ↩︎

  10. The degree of bending is governed by Snell's Law: \( n_1 \sin(\theta_1) = n_2 \sin(\theta_2) \), where \( n_1 \) and \( n_2 \) are the refractive indices of the two media, and \( \theta_1 \) and \( \theta_2 \) are the angles of incidence and refraction, respectively. ↩︎

  11. Modern equipment can detect thousands of Fraunhofer lines in sunlight! ↩︎

  12. This is because of a strong emission line at 589 nanometers, known as the sodium D-line. ↩︎

  13. Things like temperature and pressure can affect absorption and emission lines, but even under ideal conditions they are not exactly reciprocal. ↩︎

  14. The equivalence of an element's absorption spectrum to its emission spectrum was first discovered in 1849 by the prolific French physicist Jean Bernard Léon Foucault, though Swedish physicist Anders Jonas Ångström (unaware of Foucault's results) came the same conclusion using Hydrogen in 1853. Hooray for replication! ↩︎

  15. One of the means by which early flame spectroscopists identified elements was to break samples into smaller pieces and examine the bits which produced the brightest colors. This process could be iterated until you got more distinct spectral lines. ↩︎

  16. The photosphere does technically surround the core, but the radiation and convection zones are two distinct layers of the sun that lie between the core and the photosphere. See Photosphere↩︎

  17. Given a telescope powerful enough to uniquely view the star's spectrum that is. ↩︎

  18. Iron is the heaviest element produced via normal stellar fusion. Heavier elements are produced in super nova explosions or particle colliders. ↩︎

  19. Helium, trace amounts of lithium, and even scarcer amounts of beryllium were also produced during the big bang. They are the only elements that were produced both during the big bang and are still being produced by other means today. ↩︎

  20. Asimov claimed that spectrum was Latin for "ghost" or "apparition", but it only seems to have attained this meaning after the 1500s (spectrum). Before then, it meant "image". Asimov further claimed in A Guide to Earth and Space that Newton chose to use the word "spectrum" specifically for the implication of "ghost", since color emerged like a spectre from white light. While entirely plausible, I'm not certain if there's any evidence for Newton's reasoning here. But it made a cool title for my post! ↩︎