# Mirror in the atomic level…

Last week, I was trying to take a tour through these mirrors and reflecting stuff. But, I failed miserably. I thought of including other wonderful things that mirror can do, then explore deeply into the atomic level. Why I didn’t do that? I’ve already told you that I have some complicated & funny memory losses. When I was writing last post last time, I suffered a blackout which is the reason why it took so long for me, to post the “post”…

## Into the atomic level…

You say, “How exactly does reflection & refraction occur in the atomic level? I know it requires quantum electrodynamics. But, can’t that be explained in understandable terms?” Of course it can be explained. Before that, let me phrase that electromagnetic waves don’t have magnetic fields. You may well shout at me, “Are you drunk?”. No, but that’s sorta truth. Magnetic fields are a consequence of electric fields along with a pinch of special relativity. (Derek & Henry have teamed up to explain how ferromagnets and electromagnets work… Check those out!!!) So, it’s these electric fields we should be concentrating for now. Now that you’re cool, we can dig deeper into the subject. Two things happen in the mirror. First, the photons refract through glass, then they reflect at the metal-glass interface.

The common explanation goes like this. A light photon interacts with an electron in the atom of the material, by which it gets absorbed and then, re-emitted. The net effect of all these absorption & re-emission is what we perceive as reflection. This is a bit misleading. Because, this isn’t what’s really going on…

## Traveling through glass

Classical electrodynamics says this. The incoming photon can be thought to have wave-like behavior. Having oscillating electric fields, it interacts with the atomic structure, and oscillates (formally, it’s called polarization) the atomic dipoles back & forth. What I mean by dipole here? The atoms can be thought of to consist of a net positive charge bunch (which is the nucleus, of course) and a negative charge bunch (the surrounding electron cloud) which can be displaced slightly in the presence of an external electric field. But, this field is oscillating. So, the dipoles are left into tremendous oscillations which in turn, cause them to emit electromagnetic radiation (an accelerating charge radiates electromagnetic waves) of exactly the same frequency, but with a slight phase shift (which has two possibilities)…

• If there’s a shift of $\pi/2$, it corresponds to a refractive index of something greater than 1, which is what’s happening in materials like glass, the actual refraction. This is also the reason for light traveling slowly in these media.
• If the shift is a $\pi$, the waves destructively interfere and cancel out each other.

A phase shift somewhere between $\pi/2$ and $\pi$ corresponds to both reflection and absorption by some amount, and that explains the visible light frequencies for most materials.

Now, the macroscopic superposition (the total) of all these radiated waves, along with the original wave, gives you a summed up wave pattern that has experienced a net phase shift, which causes it to lag behind the incoming wave (which also explains the reduced speed). This whole mix up, is the observed beam of light that’s refracted and specular-reflected. Question: “Why does the frequency stays the same during these photonic interactions?” Think of this. As there’s no such thing as conservation of photon numbers, the photons can be destroyed and created. But, there’s a constraint. Either the photons are absorbed by the material (destructive interference) as a whole, or just transmitted (refracted or reflected) as a whole.

For example, in a dielectric material like glass (where there are no free electrons), the oscillating electric fields in the wave simply shakes the atomic dipoles back & forth, which causes them to radiate their own electromagnetic waves of the same frequency. “Why?” I’ve told you. Photons are either absorbed as a whole or just left out untouched. There’s no partial absorption, like 40% is sucked up from this photon’s body while 60% is left free (leading to the decrement in 40% of the energy, which is frequency). Meh… That’s nonsense..!!! Okay, now the forward radiation (a fancy name for the thing that’s going along the direction of the incoming wave) from these dipoles have a phase difference of $\pi/2$ with the incoming wave, which we perceive as the refracting beam. The backward radiation (going in the opposite direction) is simply the reflection (4% for glass) on such materials (like water, glass, etc.). “What about the sideward radiation?” They follow all sorts of complicated paths and cancel out one another. So, we don’t really have to worry about them…

In case of metals (which have valence electrons), the oscillation of the free electrons in the dipoles make the situation more complicated that they cause the dipoles to emit a forward radiation that has a phase difference of $\pi$, which leads to destructive interference, while the backward radiation is perceived as the reflected beam.

## Quantum laws run the whole movie…

Is that all? No, it’s confusing. How? One question. How do these dipoles exactly know where to put the photon back? We’re observing specular reflection everyday, and it happens as per the laws of reflection, that the angle of incidence equals the angle of reflection. So, how does it know where to emit the photon, while it’s busy whizzing around here and there in the lattice? It’s not just one. All the gazillion of the terrible things do the same. How is it that all those are synchronized so well?

Answer: The dipoles are not at all synchronized. The photon emission is a random process and it can be emitted anywhere, towards some angle which doesn’t agree with the law of reflection, even towards the source itself. Woah…

This issue was once addressed by Sixty Symbols (they’ve really tried very hard…)

This is where quantum electrodynamics rushes in. That’s why I told you to watch QED lectures last time. Anyways, the theory goes like this. Firstly, it just doesn’t make any sense to speak out that a photon interacts with a specific atom, nor it follows a definite path. It’s a quantum particle. It can interact with all the atoms, or take all the possible paths it can, and you can’t say anything about it. In the meantime, what we can do, is compute the chance (i.e) how likely the photons choose a specific path, after making a hell lot of observations on the occurrence with photo-multipliers and stuff. As far as I’ve seen, this is really a good explanation, based on the QED lectures, addressing Feynman’s path integral. I’m not going into it right now (as I’ve already suggested you to watch his lecture). But, this is what it roughly states…

We don’t go around defining a particular direction or path for the photon. As we can’t measure which atoms exactly the photons interact (i.e) where exactly they get scattered, we just calculate the superposition of all the possible outcomes. Though the probabilities of a specific photon interacting with individual atoms are small, the whole thing summed up for all the atoms in different layers of the material (different contributions) comes out to be a vast number. So, when we do this mathematical treatment, it just turns out that the the summed-up contributions of all possible paths of the photons is the path that has the shortest time period, which is the one that obeys $\theta_i=\theta_r$

It should be noted that this is a collective phenomena. I mean, there’s no such thing as, “a photon interacts with an electron“. It can interact with a lot of electrons, all at once. And, it does. But, you can’t observe it. The interactions lead to corresponding phase differences, that either add up or cancel out as a whole (interference). The whole business going on here, can be burned down to a single technical phrase. A photon follows a geodesic path, which simply is a straight line in a 2D flat space (which isn’t really necessary here, but I can’t resist).

Inspired by this post written by Chad Orzel (a professor) at Physics Stack Exchange.