Refraction of different wavelengths in atmosphere

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Flumble
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Refraction of different wavelengths in atmosphere

Postby Flumble » Tue Mar 08, 2016 4:24 pm UTC

According to this tool radar waves get refracted more than visible light. (assuming I interpret the longer distances for radar correctly) But in prisms, you see that longer wavelengths get refracted less than shorter wavelengths.

What kind of trickery does the atmosphere do?

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Re: Refraction of different wavelengths in atmosphere

Postby Xanthir » Tue Mar 08, 2016 8:48 pm UTC

I don't think that's a valid reading of the results. Visible light is minimally refracted by the atmosphere, so it's more or less just line-of-sight distance, eventually cut off by the curvature. Radar bounces off the ionosphere, so you can "bank" a signal a little further around the earth.
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Re: Refraction of different wavelengths in atmosphere

Postby thoughtfully » Wed Mar 09, 2016 12:10 pm UTC

Most of the time the sun is more or less overhead. When it's close to the horizon, you notice the refraction.

But yeah, the ionosphere is going to make this problem about more than just refraction.
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Re: Refraction of different wavelengths in atmosphere

Postby Twistar » Wed Mar 09, 2016 5:43 pm UTC

Flumble wrote:According to this tool radar waves get refracted more than visible light. (assuming I interpret the longer distances for radar correctly) But in prisms, you see that longer wavelengths get refracted less than shorter wavelengths.

What kind of trickery does the atmosphere do?


Basically, from your understanding of the prism, you've drawn the conclusion that index of refraction always increases with frequency (shorter wavelength diffracts more). This is not true in general for a variety of reasons. If you plot index of refraction versus frequency you will see that there a frequencies where the index of refraction is increasing and regions where the index of refraction is decreasing. Now, with optical versus RF electromagnetic radiation in the atmosphere you're talking about two frequency bands which are very far separated in frequency so there is a lot of room for the index of refraction function to wiggle up and down in between the two bands. This means that there is no reason to suppose the index of refraction is larger for visible than it is for RF. In other words, your intuition from a prism does NOT generalize.

I will state a couple facts without justification that you might find interesting. If you restrict yourself to looking at narrow regions of the electromagnetic spectrum you for the index of refraction function you will see that MOST of the time the index of refraction increases with frequency. This is called normal dispersion. However, around frequencies where the material you are considering has absorption peaks you will see sharply defined regions of the spectrum where the index of refraction DECREASES with increasing frequency. This is referred to as anomalous dispersion. Your initial assumption about this situation was that there is no such thing as anomalous dispersion. The reason we see regions of anomalous dispersion at the same frequencies as absorption can be shown using something called the Kramers-Kronig relations which relate the index of refraction of a material to the absorption of that material. Basically the phase shift light sees when it goes through a material is related in a special way to the absorption that the light sees.


The take away is that the index of refraction is determined by the atomic, molecular, and structural properties of whatever medium you are considering (in this case glass or atmosphere). The properties are in general quite complex. There are a lot of different things that can happen when you shine light on the medium. The atoms in a molecule can vibrate against eachother, the molecule can rotate, you can excite atomic or molecular electron transitions you can cause a crystal lattice to wiggle around, etc. All of these different processes contribute to the shape of the index of refraction versus frequency function so since matter is typically complicated, we find that over broad frequency ranges index of refraction functions are also complicated.

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Re: Refraction of different wavelengths in atmosphere

Postby Flumble » Wed Mar 09, 2016 7:46 pm UTC

Thanks Twistar! I was indeed under the impression that the refraction index would be proportional to the frequency.

Twistar wrote:If you plot index of refraction versus frequency you will see that there a frequencies where the index of refraction is increasing and regions where the index of refraction is decreasing.

Do you know of one for a standard atmosphere? I'd really like to see one. The best I've found yet is a diagram for water, which shows a very significant increase in refractivity for longer (radio) waves (and also the funky "less than 1" index resulting in phase velocities faster than light). But that's water, not air.


BTW, a look at the source code of the tool shows an Earth scaling factor of 4/3, which agrees with "the common trick" explained in this article to account for RF refraction.

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Re: Refraction of different wavelengths in atmosphere

Postby Twistar » Wed Mar 09, 2016 9:51 pm UTC

You know, in trying to respond to this I spent a lot of time looking for a plot of the broadband index of refraction of our atmosphere and couldn't find one. Astronomers probably have a good graph of that somewhere. But that aside, I think there is another layer of complexity which thoughtfully was referring to. The atmsophere is not completely homogeneous. As you move up or down in altitude the molecular constituents will change and this will manifest itself as a non-uniform index of refraction, so maybe it doesn't make sense to just give a simple plot of index of refraction versus wavelength for "the atmosphere", and more complicated models need to be considered.

Just to clarify, many things happen as a function of altitude. The temperature and pressure both change, the molecular makeup probably change, and other effects from the upper atmosphere probably come into play. For example, in the ionosphere high energy radiation from space can actually ionize particles whereas in the lower atmosphere this cannot happen since all of the high energy radiation has already been absorbed. EM radiation can interact differently with ionized gas than with neutral gas and this will again manifest itself as a change in the index of refraction.


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