# Shimmering from heated air and the speed of light

A few months back, I was using binoculars to check if my friend was on his boat, which was around 2 to 3 km out to sea from the shoreline where I was standing.

The images from, say the sail of the boat, were travelling at the speed of light into my eye, that's ok, no problem there.

On the direct line of sight between the boat and myself was a region of sun heated rising air, which made the image of the boat shimmer, again normal enough.

My question is based on my misunderstanding of light refraction I know, but it is as follows:

Say the column of heated air was rising at, arbitrarily say 2 metres per second, and the speed of light is vastly faster than that, 300, 000 meters per second.

In still air, I assume (and this is where I go wrong I guess), where there is no shimmering effect, that photons travel either between the molecules of air straight to my eye, or sometimes some of them will be absorbed by the air molecules and then remitted, after a very short space of time, onwards to my eye.

So my question is, given the speed of light compared to the speed of the rising air, and given the short time interval between absorption and reemission of the photons, how does the shimmering effect occur?

Is it because of scattering, that is, the photons absorbed by the air molecules are deflected away from my eye centre, giving the impression that the boat is displaced from it's true position? In other words, the photons come "into" the molecule at one angle and are reemitted at another?

My reasoning is probably wrong, but I haven't covered optics, mirages and refraction for a long time, and I am trying to understand this on on a micro level.

Anybody feel like a quick basic refresher explanation in basic refraction, or just point me at a source for explaining shimmering effects at the atomic level.

• The temperature differences change the index of refraction and that acts like random lenses with very long focal length, but since you are a long distance away, hundred of meters or even kilometers, the optical changes in the light's path are sufficient to be visible. If you do this with monochromatic light (e.g. from sodium street lights), the effect is even more enhanced because of interference. One can use this effect to measure optical inhomogeneities with amazing resolution, by the way. Look for Schlieren photography: en.wikipedia.org/wiki/Schlieren_photography. Jun 9 '15 at 22:46
• If you want to see really interesting stuff, do a Schlieren experiment. They are easy and eye-dropping, once you get it right. Jun 9 '15 at 22:55
• Might be. I had some people ask me about auras like 20 years ago... and they were very disappointed that I was making a face. :-) Jun 9 '15 at 23:30

In still air, I assume (and this is where I go wrong I guess), where there is no shimmering effect, that photons travel either between the molecules of air straight to my eye, or sometimes some of them will be absorbed by the air molecules and then remitted, after a very short space of time, onwards to my eye.

The confusion comes from mixing two physics frames/models in one sentence.

Photons belong to the quantum mechanical framework. Refraction belongs to the classical electrodynamics of electromagnetic waves. It is true that the classical emerges smoothly from the underlying quantum mechanical framework, as a meta level, and this can be shown mathematically.

In classical electrodynamics, refraction happens because of the changes in the index of refraction, and the velocity of light changes in the medium according to that index.

At the quantum mechanical underlying level, the popularization of absorption and reemission of photons model is not what is happening in transparent materials. Let us take a transparent crystal for its obvious quantum mechanical form.

A photon impinging on the crystal face sets up a quantum mechanical boundary value problem. The total state function of the crystal + photon has a probability for the photon to go through elastically, not losing energy, at all angles. In transparent materials, that probability is very large in the direction of refraction of the total wave built up by zillions of photons. In a sense, the classical wave behavior is the probability distribution, of the solution of the underlying quantum mechanical boundary condition problem, "measured" by the zillion photons.

The same is true for air when the photon meets a varying index of refraction (density etc.). The state function describing the region + impinging photon has probabilities for the photon to go through, scatter elastically, at certain angles, which is maximum in the direction of refraction.

• Thank you very much Anna. I do appreciate that the classical regime of refraction is more relevant than QM concepts in the above question. On a different, and to me more important topic, would you agree that the concept and definition of "vacuum fluctuation" means different things to different people? I asked a (yet another:) naive question on this yesterday and the links provided seemed, on first reading to me at least, to show that the phrase "vacuum fluctuation" is not an easy concept to get a consensus on. I want to ask a question on it but this time I want to word it properly. Thanks
– user81619
Jun 10 '15 at 5:13
• I think that the checked answer here physics.stackexchange.com/questions/146003/… is the physicist way of seeing this and I do not think there is a disagreement Jun 10 '15 at 5:30

Air doesn't absorb and re-emit light as you're proposing; it is (basically) transparent.

The shimmering you see is due to the varying indexes of refraction of the varying temperatures of air. When light passes through refraction gradients (which are here caused by the air temperature gradients) where the gradient isn't perpendicular to the light, the light bends. Since the warm air is rising in many columns, and cool air is falling in a similar number of columns, the refraction gradients are constantly changing, and so the path the light takes is constantly changing. So, you see your friend's boat at different (or even multiple) locations over time.