Everyday Physics is back from the holiday break, this time with a bit more complicated topic—I promise there is a very easy experiment you can do in your own kitchen to help it make sense, though.
In addition to being the mode through which we view the world, light is integral to a number of different devices we use every day, from telecommunications to microwave ovens to radios. Many of these applications came about as scientists and engineers learned something fundamental about the behavior of light so that they could turn it towards some useful goal.

One such goal is fingerprint scanning—nowadays it can be done with a number of different techniques, but one of them takes advantage of one of the stranger qualities of light. Even though it’s a little complex, you can see this effect yourself with a simple experiment you can do in your own kitchen! I’ll tell you how at the end of the post.

Light will both transmit and reflect when it encounters a new material

As we’ve discussed before, light is a traveling, oscillating electromagnetic wave. When light moves through a material it does so by affecting the atoms of that material with its electric field, and the atoms will respond in different ways depending on their surroundings (e.g. crystal structure) and the frequency of the light. Physicists lump all the different response effects into one variable called the index of refraction, n.

One of the first things to know about light is that when it encounters a material with a different index of refraction than the one it’s currently traveling through, a few things will happen: some light will get transmitted into the new material, some will be reflected away, and some might be absorbed by the new material (say, as heat energy). For now we’ll assume we’re dealing with a material like glass, where not too much visible light gets absorbed. The amount of light that gets transmitted and reflected, though, depends on the angle of incidence and the indices of refraction of the new and old material. This is shown in one of the simplest optical equations: Snell’s law, which deals with refraction, or the bending of a light ray when it encounters a new material. The equation looks like n1 sin⁡(θ1)=n2 sin⁡(θ2), where n1 is the index of refraction before the interface between materials, n2 is the index after the interface, and θ1 and θ2 (Greek letter theta) are the incoming and outgoing angle with respect to the interface.

Snell's law image

At some angles of incidence, nearly all of the light is reflected—this is called total internal reflectance

If you’re a little familiar with trigonometry, you know that sin⁡θ can never be bigger than 1 or less than -1. What this means is that if n1 is much bigger than n2, so that n1 ⁄ n2 is bigger than 1, then there is no angle θ2 that satisfies Snell’s law. This is a mathematical way of saying that no light can transmit into the new material, and instead it all gets reflected. Light that comes into an interface at an angle where this effect occurs is said to undergo total internal reflection.

Now the equation is correct, but it’s important not to just trust the mathematics blindly, especially if you aren’t familiar with where the equation comes from. What physically is going on that prevents light from transmitting in this case? Well it turns out to have to do with the nature of light moving into the new material—light propagates by polarizing(link) the material it’s moving through, causing that polar atom vibrates a bit, which emits more light. In general a bigger index of refraction means light has a tougher time wiggling the atoms. The angle matters too—it turns out that this re-radiation of light by the wiggling atom is easier to do in certain directions, and at steep angles the re-radiation is inhibited.

Even during total internal reflection a little bit of light tries to transmit—this is called the evanescent wave

Really, though, the light doesn’t just reach this interface at the appropriate angle and decide it can’t go any further—some of the light tries to get through, and is inhibited by the atoms in the new material. It takes a little bit of distance for this to happen though—this distance is called the skin depth, describing the very thin layer (typically only tens of nanometers thick in a metal, for example) into which light will propagate even though most of it reflects. In fact, if you can make a metal thinner than its skin depth (which is difficult, but possible with modern techniques) it will be transparent just like a glass window.

We call the little bit of light that moves into the skin depth the evanescent wave, because it’s sort of a ghost wave—you typically would never know it was there, unless…

Putting another material extremely close to the evanescent wave region will now allow it to transmit, and you’ll see a reflection from this third material

Here’s where the interesting part comes in—if you place a third material just behind and incredibly close to the second material, and if this third material has an index of refraction higher than n2, then this evanescent wave will reach through the second material to the third material, even though it couldn’t do this with no third material there! This effect is actually pretty close to quantum tunneling, where subatomic particles can move through regions of space that they normally wouldn’t be able to because there’s some small difference in the system—but that’s another post.

Frustratingly awesome physics

This effect is called frustrated total internal reflection, because the light would normally all reflect except that the presence of the third material lets a little bit of the evanescent wave through. The amount of light that gets through is very sensitive to the distance between the third and second material, which makes it useful for some optical applications.

The depth of your fingerprints is the right size to allow evanescent waves to reflect from the ridges but not the valleys

As luck would have it, the difference in height between the ridges and valleys of your finger is in the right range to turn this frustrated total internal reflection on and off. This is one of my favorite optical effects because while its explanation can get very technical, it’s very easy to see: just take a clear glass of water that’s mostly full and hold it in one hand. If you hold the glass up on a level with your eyes, you’ll see right through it. Now lower the glass, keeping your eyes on your fingers on the other side. Eventually you’ll be looking through the top of the water to the back side of the glass, where you’ll see a mirror surface now instead of seeing through the glass—this is total internal reflection kicking in because you’ve increased the angle.

Fingerprint science

But take a look at your fingers holding the back of the glass—you can now see your fingerprints! This is because there is a very small amount of air between the glass and your finger ridges that is acting as a third material to allows the evanescent wave to move through that air and reflect from your fingertips. The valleys of your finger are too far away to allow this, though, so you still see a mirror surface there.

If you set up a camera to take a picture of the fingerprint, you could then scan it into software and analyze the pattern just like in the crime shows. Taking advantage of frustrated total internal reflection in this way is exactly how some fingerprint scanners work. Try it yourself!

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