Talk:Rayleigh scattering

Rayleigh scattering (named after Lord Rayleigh) is the reason why the sky is blue. Rayleigh scattering of photons by Earth's atmosphere is dependant upon the size of the particles causing the scattering and the wavelength of the photon being scattered.

Neither of these first two sentences actually says what Rayleigh scattering is. The first says that it's the reason why the sky is blue. (So, now we have a name to a scientific explanation, but not the explanation.) The second says that the scattering is dependent upon something or other, but we still haven't been told what it is that is so dependent! --LMS

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Have someone informations about Rayleigh's "blue sky law"? -- looxix 21:57 Mar 18, 2003 (UTC)

Why is Sky Blue? Answers

The question is not answered very well. Why not green or another shade of blue? The answer seems more dependent on the absorption of energy and the re-emission of a photon from the oxygen molecules, which is blue. The emission spectrum of the other gasses that make up the atmosphere are outside of our personal visual range. Another interesting question is, was the color of the sky always blue? I think not, as the content of the atmosphere has not always contained the 20% oxygen.

Although there is an absorption/emission line for doubly-ionized oxygen (O-III) at 500.7 nm, which is indeed in the blue-green, that is not responsible for the blue color of the sky, since other gases will also produce a blue sky, provided that the gases are present in sufficient quantities and the light source is bright enough (which the Sun surely is!). It is, as the article states, essentially a scattering effect.

Classically, atmospheric molecules can be treated as dipoles, which react to incident light much the same way that a spring reacts to an applied force. So long as the frequency of the stimulus is considerably below the resonant frequency, the amplitude of the response is proportional to the square of the frequency. The intensity is proportional to the square of the amplitude, so the total scattering is proportional to the fourth power of the frequency. This very rough treatment assumes the dipoles are of negligible size compared to the light waves, so (for instance) raindrop scattering does not obey the fourth-power law; rather, it follows Mie scattering, which is much less dependent on frequency and accounts for the generally grey or white color of clouds.

Note that the fourth-power law doesn't depend on the specific gas--it only requires that the resonant frequency be much higher than that of the incident light. That clearly is true for nitrogen, for instance--otherwise, we wouldn't be able to see sunlight through the predominantly nitrogen atmosphere. So a purely nitrogen atmosphere would also produce a blue sky.

As to the color of the early sky, in a reducing atmosphere containing hydrogen, water vapor, methane, ammonia--I don't really know. The Sun might have appeared bluish to our eyes, since hydrogen, methane, and ammonia all have absorption in the 600 to 900 nm range. (Uranus and Neptune appear bluish for a similar reason; their atmosphere absorbs the red light and reflects the blue light back to us.) The Sun was some 25 percent dimmer then, too, and emitted proportionally less blue and violet light. Possibly it would have been kind of dark (although our brains are very good at compensating for large changes in luminance and color balance). My guess is that the sky would have been blue back then, as it is now. BrianTung 23:17, 2 January 2006 (UTC)

The following paragraph (which was not written by me) I cut from the article, because its place is in the discussion.
The article is generally correect but light scattering depends on anosotropy. Anisotropy is the phenomenon where the speed of light in one direction is different in another direction usually perpendicular sources Nitrogen, the major source of gas in the atmosphere is isotropic. However there are small quantum fluctuations in the isotrpoy of nitrogen where it becomes anisotropic. This microscopic fluctuating is actually the source of the scattering on which the Rayleigh scattering and theory is based. Any comments?
Synapse 18:43, 10 January 2006 (UTC)

From the mailing list

>Dear Sir or Madam,
> 
> On that link to the rayleigh scattering coefficient ks is a mistake in
> the power of pi. Pi should be to the power of five and not to the power
> of six.
> http://en.wikipedia.org/wiki/Rayleigh_scattering
> 
> Please check this again. Thank you.
> 
> Best regards,
> Daniel Ploss

Can anyone find a reference to confirm this? -- Anon.

I changed it to to the 6th after some looking on Google. 69.142.2.68 10:51, 30 August 2005 (UTC)

The original reference for this article [1] has the "5" and "6" transposed between π and d. I've now re-written the maths from a solid reference, and I'm confident that it's now correct. The bottom two sections are still really chatty, though. -- DrBob 01:59, 31 August 2005 (UTC)

I found a different formula for Rayleigh scattering.

I found a different formula for the Rayleigh scattering coefficient. There the number of scatterers is in the denominator. It is from a lexicon of optics. I doubt that this is wrong. The formula is scattering coefficient b = (8*PI^3/3*N*lambda^4) * (n^2-1)^2, where N is the number of scatterers and n is the index of refraction.

Since that formula doesn't contain a term for the size of the particles (d in the article), it's probably only valid for the limit of d<<λ, so it's valid in a different domain. I'll try to check. -- DrBob 14:45, 11 Oct 2004 (UTC)

Could you please give the source for the formula in the article. Thank you.

Why is the Sky Blue?

It should be mentioned that Raleigh Scattering is not physically a result of the size of the particles encountered by the light, but rather a result of interactions with the electron structure of the atoms (primarily a quantum mechanical interaction).

Simply put, the idea that size of particulate as being the primary physical reason for scattering in our atmosphere is no longer a modern view. This idea can't even be considered simplistic, because it is physically incorrect. While, Raleigh did observe the connection between scattering and size of the particle, this is not the reason for the scattering nor for why the sky is blue. Raleigh scattering is an easy to use formula and certainly important, however we shouldn't go too far - someone needs to explain that this effect does not consider light matter interaction as modernly viewed and that it posses Cretan inherent assumptions including the fact that spacing of particles is not considered. Application to atmospheric color should be amended to stress that the electronic structure of the particles, as governed by quantum mechanics (alternativly known as chemistry), describes the scattering of light in our atmosphere approximated by Raleigh Scattering.

Since no mention of where Raleigh's equations come from or when they are created are mentioned the reader is free to believe that his equations are modern and that the interpretation of them is the modern view. This is a serious oversight, because rule of thumb equations like this one often are often modified as theory develops. Lord Rayleigh's result was not fundamentally derived from more modern theory of quantum mechanics, which describe the interaction of light with matter.

Ultimately the question,"why is the sky blue?" is a matter of light - matter interaction, not light size interaction as this website asserts.

Furthermore, Raleigh's assumptions are not indicated here! How is the reader to know what circumstances his equation are valid for? I see no mention of pressure dependence which would effect spacing between molecules. Light when viewed as a wave must be considered to be able to diverge when passing through a gap on the order of a specific size, which would be effected by pressure.

Confusion of Terminology

You can't use terms from modern theory like "photn" in a document describing a theory that was developed prior for many reasons: 1. it creates ambiguity as to how modern the theory is 2. it suggests to the reader that the theory interprets light as photons, in fact the theory does not 3. it implies that the author at least heard the word photon before he died, this however is not possible

Simply put the use of the word photon in this context is confusing and erroneous. Consult any modern physics text book for confirmation. Suggestion (tippler and lewellen).

What's wrong?

The intensity I of light scattered by a single small particle from a beam of light of wavelength λ and intensity I₀ is given by:

$I=I_{0}{\frac {(1+\cos ^{2}\theta )}{2R^{2}}}\left({\frac {2\pi }{\lambda }}\right)^{4}\left({\frac {n^{2}-1}{n^{2}+2}}\right)^{2}\left({\frac {d}{2}}\right)^{6}$

where R is the distance to the particle, θ is the scattering angle, n is the refractive index of the particle, and d is the diameter of the particle.

So the smaller the diameter of the particle the less of the input beem goes out again. Particles of vanishing diameter would absorb all light, really big particles would emit more light than they receive.

What's wrong? 84.160.230.81 19:02, 5 October 2005 (UTC)

• Nothing is absorbed. Any light that isn't scattered is transmitted straight through. The equation gives the intensity of the scattered light, only. Vanishingly small particles will not scatter. Also, the equation is only valid for d < λ/10 (as stated in the article). Consider that R must be at least as big as d; therefore the scattering coefficient is always smaller than 1 in the valid range. -- Bob Mellish 19:18, 5 October 2005 (UTC)

More about S-Matrix

It would be very nice to have some "further reading", maybe some URLs or something like this about the S-Matrix.

Rayleigh's Criterion

would this also be the page to add something about Rayleigh's Criterion? i just learned about it in class, and came here to see if there was more information. it has to do with the angular seperation of light sources and weathe ror not lenses can resolve the images of the two... heres a link to a page with more information on it ( http://www.fas.harvard.edu/~scdiroff/lds/LightOptics/RayleighsCriterion/RayleighsCriterion.html i wouldnt feel comftorble writing something myself on it seeing as i just learned about it

• We already have information about it at Rayleigh criterion. It's not anything to do with scattering, so it doesn't belong in this article. --Bob Mellish 21:31, 19 December 2005 (UTC)

RC CLARK's edit

The article is generally correct but light scattering depends on anosotropy. Anisotropy is the phenomenon where the speed of light in one direction is different in another direction usually perpendicular sources Nitrogen, the major source of gas in the atmosphere is isotropic. However there are small quantum fluctuations in the isotrpoy of nitrogen where it becomes anisotropic. This microscopic fluctuating is actually the source of the scattering on which the Rayleigh scattering and theory is based. Any comments?

This belongs in this section Daemon8666 20:23, 13 January 2006 (UTC)

Typical values for Earth's atmosphere

Does anybody know typical values for n and d in the atmosphere of Earth? Is the refractive index of the particle the same as that of air (approx. 1.0003 at sea level), or is a different value to be used for a single particle? In general, it would be nice if one could use the formula along with these values to make calculations with these. Getting information via Google about this seems to be very difficult (either the information is only about the principle but without numbers or it is drowning in details or you have to pay for it or Google's hit is about a completely different topic), so it would be nice if Wikipedia could provide such useful information. If I had such information I surely would add it to the article, but unfortunately I don't have any.--SiriusB 20:24, 26 January 2006 (UTC)

The "cleanup" tag

The section "An explanation of Rayleigh scattering using the S-matrix" appears to have been written very casually. I am in favor of deleting it and taking a fresh start to add more theory, if it is needed. I deleted one error, but I think there are too many others to fix easily. David R. Ingham 21:26, 14 March 2006 (UTC)

Oxygen is blue.

I understand oxygen is blue. Why is this omitted from the discussion?

Where are the experimental measurements associated with the support of the grand boggling mathematics? Some of us are wary of those who tend to "get lost in the mathematics".

"Logic is a systematic method for getting the wrong conclusion...

with confidence."

A scientist can never afford to discard data, however contradictory it may be to his ideas and intentions.

Edit: (Sometime around Wednesday, April 20, 2006) My apologies for talking. I presented no data. I do not have access to the necessary spectroscopy equipment.

I wonder if there is any argument that ozone is blue.

I also wonder if there is any debate over why a gas flame is blue.

I also wonder if there is any debate over why there is some blue gas just beneath a candle flame.

I also wonder if a piece of white paper held a distance of approximately one kilometer is blue (one kilometer having about as many oxygen molecules in a path as two inches of liquid oxygen, which is generally agreed to be blue.)

I am eager to see the experimental measurements that support the theory of Rayleigh scattering.Coucilonscienceorg

The color of liquid (and solid) oxygen is blue, with the solid being somewhat darker than the liquid. The same is true of ozone, with both liquid and solid forms being darker than they are for molecular oxygen. Solid ozone, in fact, is so dark as to be almost black.

This gives a clue as to why these facts, however true, are omitted from the discussion. They are irrelevant. If the sky were actually blue because of light absorption (which is why liquid oxygen is blue), the atmosphere would be opaque to the point that the stars could not be seen at night. In truth, though, they look nearly as bright as they do from above the Earth's atmosphere. So the sky must be blue for reasons other than the absorption of light by molecular oxygen.

The sky on Mars, when it is relatively free from dust, is blue-violet, and its atmosphere contains no oxygen to speak of; it is thin and consists mostly of the colorless gas carbon dioxide. When carbon dioxide condenses, it goes through no liquid phase at Martian pressures and freezes directly into colorless dry ice. So the color in the skies of Mars also cannot be due to the color of oxygen.

As for "getting lost in the mathematics," while it is true that some scientists do over-formalize, it is important to remember that they are caught at that by people who specifically understand that mathematics. And when they do so, they point out either what is wrong with the mathematics, or why it is inapplicable. It is an error to say, "Wow, that's a lot of math," and simply by virtue of that impeach the reliability of that math. You have to show why it is wrong or inapplicable. Not being able to understand it is no excuse, since by this point, there are lots of people who do understand the math.

In short, just because one doesn't understand an explanation, does not mean the explanation is wrong. It is quite conceivable that one's understanding is insufficient. And when an explanation is commonly accepted by people who are trained in experimental science, it becomes more than conceivable--it is almost inevitable. That insufficiency can be repaired, of course, but you can't expect it to happen in a single afternoon, or without effort. BrianTung 23:35, 25 April 2006 (UTC)

I apologize for being stupid. The question I am asking is where the experimental evidence for the particular intensity of the particular blue color we see in the sky. In this entire discussion, noone has mentioned a single reference to experimental verification that Rayleigh or any other type of scattering could produce the particular intensity of the particular blue color we see in the sky.

Furthermore, what is the predicted intensity of color we would perceive from this scattering? How can it be explained that the blue of the sky matches the 500.7 nanometers of the strong emission line of doubly ionized oxygen? I see that there are references to evidence that the sky on Mars is blue. might that evidence can be shared with us?Coucilonscienceorg 08:50, 28 April 2006 (UTC)

Oxygen is not blue

I can not even begin to address the fundamental misconceptions presented in the previous comment. Anyway, now that that is out of the way, I cleaned up the s-matrix bit a fair amount, still needs a bit of proper prodding, but should be bordering on acceptable. --Meawoppl 05:41, 18 April 2006 (UTC)

Emission spectra

If the atmosphere of a planet contains atoms or molecules with particular emission spectra, will the sky of the planet be the color of the emission spectra, or the color of the scattering? Perhaps some of the excellent astronomers present can present some data in this regard.Coucilonscienceorg 09:48, 28 April 2006 (UTC)

The variaty of the universe is infinite, and one can think of many different planets and circumstances. The color of the star(s) is also of importance. How the sky would look under different circumstances can be calculated. If for example you would have a very red star, the sky would still not be red as you might think, but rather the same blue in zenith but fading to a rather reddish brownish color near the horizon.

Again, this is not relevant on earth where the sun is has a nice white-yellowish color. Albester 13:04, 10 May 2006 (UTC)

The main reason light from the sky is blue

If Rayleigh scattering is the "main reason" for the blue of the sky, what are the other reasons? Why aren't these other reasons mentioned anywhere?Coucilonscienceorg 01:55, 1 May 2006 (UTC)

It is the main reason,and in the case of earth the only reason. What you mentioned earlier about oxygen being blue in liquid state etc simply have no bearing on the question of why the sky is blue. I don't mean to be rude, but I find your comments about logic and mathematics insightfull as to how you think, but that opinion is not shared by many, has no acceptance among serious persons and as such they should not be put here on wikipedia. Perhaps you can start your own webpage explaining your own theories? Albester 12:59, 10 May 2006 (UTC)