A light-hearted paradox: why can’t we see through walls?

I’d like to start by asking a question: Have you ever been inside of a building and made a phone call to someone on your cellphone? If you have, I bet you were able to hear the person on the other end relatively well.

hear_through_walls

Did you know that your cellphone actually sends and receives digital information via microwaves emitted from your phone’s antenna? Furthermore, are you surprised by the fact that these microwaves, a form of Electromagnetic Radiation, actually pass through the walls of the building as they travel to the nearest cell tower? You should be!

Maybe the “surprise” would be more obvious if I asked you a second question: Have you ever been inside of a building and seen the people standing on the other side by looking through the wall?see_through_walls

I’m going to guess you haven’t. And, in case you don’t already know, we see visible light, yet another form of electromagnetic radiation.

But wait! What’s going on here? We just identified that microwaves and visible light are both forms of EM waves, yet the walls seem to be almost transparent to microwaves and completely opaque to visible light. Why is this so? Why can we receive phone calls inside of building but not see through walls?

The answer to this question is not complicated, but perhaps somewhat counter intuitive (Oh physics I do love you for that!). In fact, the only thing we need to answer this question is understand the 3 possible ways light can interact with an object. To illustrate, what do you think could happen if I shined a beam of light onto a surface? What could the light do?

light_interacts_with_object

Well, either you guessed it or the diagram gave it away, but the light could either scatter, get absorbed, or transmit through the object. I want to expand a bit more on scattering and absorption but, before I do that, I want to provide you with an intuition about transmission first.

Transmission

To me, it always seemed a bit crazy how light can pass through a solid mass; it must be bumping it to something right? Well if you are confused like I was, you can think about transmission as the process that happens by default if the light does not get absorbed or scattered. In other words, since energy is conserved and light is energy, if the light does not get absorbed or scattered, it can’t just disappear so it simply continues traveling onwards, through the object and out the other side.

Scattering

Okay, now that we’ve addressed transmission, let’s talk about scattering and what it is. Technically, scattering happens when a beam of light hits a non-uniform surface causing individual waves to disperse in different directions. However, this definition does very little to build up our intuition for predicting how much and which types of EM waves are likely to to scatter.

I think a better explanation would be to make an analogy between scattering and riding along a bumpy dirt road. To begin, imagine we were to ride along this dirt road on a child’s tricycle. Let’s say that the bumps in the road are actually quite large and are roughly as deep as the height of the tires on the tricycle. Will riding across this road in a tricycle be a pleasant or unpleasant experience?tricycle_dirt_roadThis isn’t a trick question; it’s not going to be pleasant at all! The tricycle is going to go up and down and probably get stuck several times too. Now, lets run the same experiment over but this time, let’s drive across the dirt road in a giant monster struck. Would you expect the ride to be as bumpy or do you expect it to be significantly smoother?monster_truck_dirt_roadIt’s going to be a lot smoother! Okay, but why? Well, as you might have guessed, the bigger the vehicle’s wheels are, compared to the height of the bumps, the less the vehicle will notice the uneven surface since the wheels will just roll over it. In this analogy, the tricycle, with its small wheels, represents visible light (very small wavelength) and the monster truck, with its very large wheels, represents microwaves (10,000 times larger than visible light).

scattering_analogy

This phenomenon is scientifically known as Rayleigh scattering, and is an important interdisciplinary concept. Essentially, the formula holds that smaller particles scatter light with a lower intensity, and with a unique dependence on the wavelength of the light being scattered gives rise to interesting consequences. Primarily, this explains why our sky is blue: blue light (shorter wavelengths) is more easily scattered by the small gas molecules in the atmosphere. The applications for this behavior range from nanopores to optical fibers, so it’s definitely relevant in many facets!

rayleigh_sunlight_scattering

Absorption

Okay, let’s talk a bit about absorption now; it’s the last tool we need to solve the mystery. Absorption happens when a particle of light has enough energy to excite an electron in an atom to the next energy level. Essentially, think about a really simple model of an atom where you have the nucleus in the center and a single electron orbiting (electrons don’t actually orbit!) an atom in the ground energy state:

excited_state

Now, if a particle of light with enough energy were to come by and smack into the electron, then the electron would absorb from the photon’s energy and get promoted to the excited state. Question: What would happen if the particle of light did not have enough energy?ground_state

Nothing! Absolutely nothing! Electrons don’t have fractions of energy levels or a continuous spectrum of energy levels (everything is discrete in quantum physics!). As a result, if the photon does not have enough energy to excite the electron to the excited energy state the photon will not be absorbed and, instead, will continue on.

This means that absorption only occurs if a photon carries enough energy to excite the electrons of an atom. If the photon does not have sufficient energy, absorption cannot occur and the photon passes onwards.

We now have all the tools we need to figure out why why we can’t see through walls. So, to bring it all together, I am going to reveal some data approximations about walls, microwaves, and visible light. Here it is: wall_factsLet’s start by examining the wall data. All this is saying is that walls are very smooth (a roughness of 1-0.1 mm is quite typical) and that they will absorb light if it has at least 1 one-thousandth of an electron volt (these are the units of energy in Quantum Physics).

If we look at the data for microwaves, we see that their typical wavelength is on the order 10-30cm. What does this mean we can predict about microwaves if they hit a wall? I’ll give you a hint in the form of another question: Will they scatter? NO! Absolutely not! Microwaves are almost 300 times larger than the characteristic roughness of the wall so the surface of the wall to microwaves is like the dirt road to the monster truck’s wheels: effectively flat.

Next, if microwaves have about 1 one-hundred-thousandth the energy of an electron volt, which is about 100 times smaller than the minimum band energies of the atoms in a wall, can we predict anything about whether the wall will absorb microwaves? You bet we can. Going back to the model of the atom, a microwaves particle does not have enough energy to excite the electrons in the wall to the next energy level so, microwaves won’t get absorbed!

We just determined that microwaves are too long to get scattered by walls and that they also don’t have enough energy to get absorbed by walls either. What is the only thing that microwaves can do then? That’s right, they can only pass through the wall. This is why we can make a phone call inside of a building!

Running a similar analysis on visible light, we see that it has a wavelength almost 1000 times smaller than the characteristic height of a walls roughness. This means visible light is easily affected by the micro bumps and irregularities of the walls surface  just like the tricycle was affected by the bumpy dirt road. As a result, when visible light hits the wall it gets scattered like crazy!

In addition, if we look at the energy of visible light, we also see that it has about 1000 times more energy than the minimum amount required to excite the electrons in wall’s  atoms. From our analysis on absorption, we would predict, then, that visible light is easily absorbed by the wall too.

Perfect! We just showed that visible light not only gets scattered easily, but it also gets absorbed readily too. If all of the visible light gets either absorbed or scattered, what do we know can’t happen??? Exactly! Visible light won’t travel through which means we can’t see through walls! Bazinga!

tumblr_ncf65okkby1qlp8eco1_500

— Devin Morgan

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