How Spectroscopy Works.


First, some definitions. You can skip these if you’re already familiar:

Spectroscopy vs. Spectrography

Spectroscopy: The field of observing spectra with your own eyes. When I put a diffraction grating on my telescope, then look through it, I’m looking through a spectroscope. Fun fact: some kind of microabberation of the lenses of my eyes causes me to see rainbow halos around bright objects. So technically, when I see those rainbow halos, I’m seeing the spectrum of the bright object…. in other words, my eyes have a built-in spectroscope!! How cool is that?!? 🙂 You will probably encounter spectroscopes made out of paper towel tubes with bits of cut up CDs as diffraction gratings; it’s a spectroscope until you hold a camera to it, at which point it becomes a spectrograph. Spectrographs include cameras by definition.

Spectrography: The field of photographing spectra. A “Spectrograph” is any device that records spectra. Technically, if I hold my phone up to the mesh curtains we have downstairs which have a diffracting effect… that’s a spectrograph! 🙂 The question of whether me sitting at a table, looking through a spectroscope and drawing what I see constitutes a “spectrograph” is an interesting one.

By the way… I’m an astronomical pedant, and the difference between the two is one of my biggest pet peeves, behind the “astronomy/astrology” mixup. That said, I’m also one of the only people in the world who will even notice if you get the two mixed up, so really, don’t lose sleep over it if you do. 🙂 Even the professionals often refer to what they do as “spectroscopy”. *twitch*

Refraction

Source: Giphy

When light enters a medium (substance; like glass, water, or air) at a shallow angle, it’s bent as a result of its speed changing. In many materials, like glass, the amount that the light bends (refractive index) varies depending on the frequency (color) of the light, so when light passes through glass the different colors separate slightly. This is how prisms work! While prisms can be used to form spectra, the preferred way of doing so in astronomy is diffraction gratings, so for the purposes of this article I’m only going to talk about diffraction gratings. I’m mentioning refraction here at the beginning so that there is no confusion between refraction and diffraction, which are two different processes.

 


Diffraction

A demonstration of “edge diffraction” with only one obstacle to bend around.

Due to the wave nature of light, when light encounters an obstacle, it will bend or “diffract” around it. Imagine straight waves in water encountering a wall with a little opening in it. When the waves pass through the opening, they will ripple out in little circles, right? Light does that, too. The bending is normally very, very slight- light coming in through a window hardly bends at all. But the smaller you make the gap, the more the light bends. When the gap becomes comparable to the size of the wavelength of light, you get very strong diffraction (bending).

Here’s why this is good for spectrography… The larger the gap is than the wavelength of the light, the less the light bends, right? And vice-versa, the smaller the gap compared to the wavelength, the more the light bends. Therefore, blue light, which has a wavelength of ~450nm, will bend less than red light, which has a wavelength of around ~700nm. So when white light passes through a small opening, each wavelength bends a little differently, and the colors separate. And that is how we wind up with spectra!! The violet light bends only a little, then the blue light a little bit more, then the cyan light even more, etc., so that we see the whole rainbow spread out next to each other.

A demonstration of diffraction with an opening significantly larger than the wavelength being diffracted.

So, that’s great and all, but that sounds like it should only give a splotch of white light with rainbow edges, right? Maybe a little bit bluer in the middle since the redder colors are being thinned out a bit. But the actual pattern that we get is weird; it looks like multiple bars or dots of light, with the brightest nested in the center, fainter ones outside that, even fainter ones outside that, etc.

Now here is where you kind of just have to trust me. Sometimes, in science, you’ll come to a “what” without a “why”. Maybe it’s something that scientists are working on or maybe not; in either case it’s a question in need of study.

A demonstration of diffraction with an opening similar in size to the wavelength being diffracted.

Maybe it’s regarded as a fundamental property of nature. If you keep asking “why”, and you’re asking someone who’s honest, even the best physicists’ answer will always wind up being “because”. Why does an apple fall down and not up? Easy! Any physicist (and hopefully most others!) can tell you that it’s gravity, that’s the why. Most people stop there, apparently satisfied (or deterred by math). But there are more questions to be asked, and interestingly kids are often the ones to do the asking. “Why does gravity make things fall down?” There are many ways to answer that question, but the deeper you go, the more you ask, each eventually traces back to… “because”. “Why?” “It just does.” Humankind might as well be a young child arguing in circles with its frazzled parent.

 


Huygens-Fresnel Principle

Back to the weird patterns on our screen. The Huygens-Fresnel Principle explains the “what”, even if not the ultimate “why”. The Huygens-Fresnel Principle states that every point on a wavefront is the source of little spherical wavelets. There are infinitely many points on the surface of any given wavefront, so the wavefront is like a “mesh” of little wavelets. The principle also states that a wavefront is a line drawn tangent to all of the little wavelets. So in a diagram, you might draw a line of spheres, which looks bumpy, but when you draw the wavefront- a line which touches, but doesn’t intersect, each of the spheres- you get a smooth surface. Then, according to the Huygens-Fresnel Principle, that surface generates its own line of spherical wavelets, and the process starts over. Or in other words, “Consider a wave front at the moment t as the source of the new (secondary) waves emanating from the points of this front. The HP states that the new wave front at a later time is the envelope of the fronts of these secondary waves”.

It seems to be debated, or have been debated in the past, as to whether this is actually, physically, what happens– but for whatever reason, it works as a method of describing the diffraction of light, so we can use it.

Imagine a flat, parallel wavefront traveling towards our wall with a little opening in it. All the time, each point on the wavefront is generating a little sphere of a wavelet, but they all wind up overlapping into a new wavefront, and the cycle continues. When our wavefront encounters the wall, much of it is stopped, but some of it makes it through the gap. This is where the little spherical wavelets come in handy! The spherical wavelets on the edges are now free to spread out, causing the light to bend around the corner, just like water waves. What’s more, the waves are now free to interfere constructively and destructively. Before, within our infinite line of wavelets, all of them were interfering, so there was no “net interference”, so to speak. But now the wavefront is out of balance; a wave on one edge might be interfering with 1/3 as many waves on the left as it is on the right, and vice versa. As a result, a pattern emerges… one bright spot or bar nested in the center, with fainter spots/bars surrounding it on either side. Sound familiar? It should. It’s the same weird pattern that we get from our single opening.


But the diffraction from a single opening is very, very small, and the colors are all overlapping. In order to create clean spectra and of an easily visible size, we need multiple openings close together. For the sake of this explanation, let’s switch out analogy from “openings” to “slits”- vertically oriented slits are the typical way the experiment is done, and the phrases used to refer to these types of experiments are almost always “single slit” or “double slit”, not “opening”.

If you use two slits, we can simplify things by thinking of each slit as emitting only one little spherical wavelet, whereas before we had to imaging a whole row of them to understand single-slit diffraction.

With two slits, as the wavelet from one slit interferes with the wavelet from the other, a pattern appears- like our pattern of bright spots, only now there’s way more of them, fading in and out of view. In fact, if you compare the patterns, you’ll notice something… the pattern you get from two slits is a “finer-grained” version of the pattern from a single slit. It’s as if you drew the pattern created by a single slit onto a sheet of paper, then took your eraser and striped it up and down. The interference pattern produced by the two wavelets is fine; with many more bright and dark bars. But the two-slit interference pattern is multiplied by the single-slit diffraction pattern that you’d get if you only had one of the slits, causing the two-slit pattern to fade in and out. So if a particular point on the single-slit pattern was only at half intensity, that point on the double-slit pattern will be multiplied by 0.5; so that even if the two-slit interference pattern had a full-brightness peak there, it would wind up only being half-brightness.

The size and spacing between the bright bars of the double-slit interference pattern is determined by how close together the two slits are; the more widely-spaced the slits are, the thinner the bright bars are, and the more fit in the pattern. The size of the overall single-slit diffraction “envelope” is determined by the actual size of the slits; the smaller the slits, the larger the pattern, just like with single-slit diffraction (remember, the smaller the slit compared to the wavelength of light, the more the light spreads out!).

Diffraction Gratings?

The diffraction from a double slit is better than a single slit for creating spectra because the peaks are narrower, so the spectrum is clearer; but it still has a lot of overlap and the resolution is not very good at all. In order to get nice, sharp, clean spectra, we need to add more slits. The more slits that you add, the narrower the peaks get. The ideal tool for spectrography is a surface consisting of nothing but thousands of slits, right next to each other, like a mesh, or… a grating! That’s right, a diffraction grating is, in essence, a surface made out of hundreds or thousands of little diffracting slits. In reality, diffraction gratings are usually not made out of actual slits that go all the way through the material; instead they’re made out of glass and “ruled” with very precise, straight grooves. Some gratings are used as “transmission gratings”, where the light passes straight through them like a weird lens; others are coated in reflective aluminum and used as “reflection gratings”, acting like weird mirrors that create spectra. In any case, diffraction gratings are the engine that powers astronomical spectrography. Plastic diffraction gratings, which are not precise enough for exacting lab work but still very good, are cheaply available, and lots of fun to play around with!

It’s all around you!

But you don’t have to buy a diffraction grating to get in on the wonderful world of spectra. I’ll let you in on a secret… all this stuff that we’ve talked about, refraction, diffraction, interference, spectra- it surrounds you, happening everywhere every day, if you only look close enough. Think about it! Every second of every day (unless you’re an astronomer), your eyes are bombarded with trillions of photons. With that much light around, some of it has to be doing something interesting, right? 🙂

There are many diffracting structures in everyday life, and you don’t have to have rainbow halos in your eyes like me to see them! Mesh curtains and screens can function as weak diffraction gratings. Think about all those tiny, parallel openings! If you have a mesh curtain or screen in your house, try looking at a bright object through it, like a glint of sunlight off a car, or a distant streetlamp. (Do NOT look directly at the sun through a mesh curtain! It will still hurt your eyes, and it’s too big to see spectra! More on that in a later post.)

Another famous source of diffraction is CDs or DVDs, though those are less common today than they used to be. Have you ever held a CD up to the light and admired the rainbow play of color across the surface? Those rainbow glints are spectra! Information is recorded on a CD by carving thousands of tiny little circular grooves into it… turning it into a big, curved reflection grating! Old CDs can make nice, high-resolution and clean spectra.

While astronomers primarily use diffraction gratings for astronomical spectrography, diffraction isn’t the only way to create a spectrum. Spectra can also be created with refraction, as in the case of a prism! Prisms are the obvious example, but many other glass or plastic objects have the potential to create spectra. Have you ever been somewhere with a window made of old-timey “beveled” glass? The cut edges of the glass are little prisms in their own right, and when the sun shines through them can cause little spectra to appear. One example which delights me is that of the lid of my Yeti cup! The thick acrylic lid has a beveled edge, shaped similarly to that of a triangular prism. When light strikes the lid at the right angle, a curving spectrum / light “caustic” is projected. (I have gotten some strange looks before by delightedly going up to someone with my Yeti in hand, holding it out and declaring “Look!”; I was trying to indicate the bright arc of rainbow projected onto my other hand, but they just stared at my cup in confusion!)

Other things, like items with holographic film inclusions, use diffraction to create rainbow effects, though in the case of holographic film the spectra are usually fractured and not very clear.


[This is an overview that I wrote to help out some of my classmates in a school-based astronomy program (Skynet Junior Scholars) that I participated in.]

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