Dear Rajat,

You are right, according to Rayleigh scattering, we should observe a violet sky. In order to understand why we perceive the sky to be blue, we should take into consideration two other phenomena:

- the solar radiation spectrum has its peak in the blue wavelengths and it drops for the violet wavelengths.

- in addition, our eyes are composed of three types of cones detecting red, green and blue colors. Thus, if you look at the sensitivity of the blue cones as a function of the wavelength, you will see that this sensitivity is much higher for the blue color than for violet.

Besides, you also asked a question about the particles that scatter the blue wave lengths predominantly. When you want to study light scattering, you use Mie theory and Rayleigh scattering is a limit of Mie theory when the size of the scattering particles is lower than the wavelength. According to Hirschfelder, Curtiss and Bird (1954) Molecular Theory of Gases and Liquids, Wiley, New York, the size of the particles present in the atmosphere is comprised between 2.50 and 5.30 nm, much lower than the wavelength. Thus I don't really think there will be a difference on the scattering properties of different the different molecules of the atmosphere for the visible wavelengths.

I hope it answers your question.

Best regards,

Thibault Cremel

Dear Rajat,

You are right, according to Rayleigh scattering, we should observe a violet sky. In order to understand why we perceive the sky to be blue, we should take into consideration two other phenomena:

- the solar radiation spectrum has its peak in the blue wavelengths and it drops for the violet wavelengths.

- in addition, our eyes are composed of three types of cones detecting red, green and blue colors. Thus, if you look at the sensitivity of the blue cones as a function of the wavelength, you will see that this sensitivity is much higher for the blue color than for violet.

Besides, you also asked a question about the particles that scatter the blue wave lengths predominantly. When you want to study light scattering, you use Mie theory and Rayleigh scattering is a limit of Mie theory when the size of the scattering particles is lower than the wavelength. According to Hirschfelder, Curtiss and Bird (1954) Molecular Theory of Gases and Liquids, Wiley, New York, the size of the particles present in the atmosphere is comprised between 2.50 and 5.30 nm, much lower than the wavelength. Thus I don't really think there will be a difference on the scattering properties of different the different molecules of the atmosphere for the visible wavelengths.

I hope it answers your question.

Best regards,

Thibault Cremel

How about this explanation, for example:

http://en.wikipedia.org/wiki/Rayleigh_scattering

Rayleigh scattering gives you the luminosity of the sky.  Rayleigh scattering gives you a blue-white color, factors being listed above including the solar spectrum, the Rayleigh behavior, and the sensitivity of the eye, but not a really blue color.  I have been assured, by a molecular spectroscopist interested in the topic, that to get from the blue-white sky to big sky blue there is also some chop-off in the far red due to an overtone line of water, in addition to which when you look at the sky through fall leaves the eye does color correction, as seen in Mondrian paintings illuminated by monochromatic or bichromatic light.

As a minor aside, there are photos of the atmosphere of Jupiter from the descending NASA probe, taken above the altitude of the clouds.  At that altitude, the Jovian sky is brilliantly clear and a gorgeous bright blue.

Thank you very much Cremel, Grabtchak and Philies for your responses. I wanted to point out how loosely many physics text books very loosely speak of Rayleigh scattering as the reason for blueness, while so many other factors are at work.

By the way,  what exactly are the particles (molecules) of the atmosphere that scatter the blue most? Could you please give some details or references ?

Regards,

Rajat

Rajat,

to my mind nobody knows the answer on your last question. You may do scientific project on this theme.

Regards,

Eugene.

Rajat:

On a "Rayleigh Day" scattering by molecules (nitrogen and oxygen) dominates scattering and extinction in the atmosphere yielding an intensely blue sky and strong polarization. This corresponds to a visibility of about 160 km. If we add fine particles, for example sub-micron diameter combustion particles, the sky is still blue, if we add large particles, for example mineral dust particles or water droplets, the sky becomes more whitish. 

So long,

Hans

Hi Hans,

Could you please give me the wavelengths of the blue scattered by atmospheric Oxygen and Nitrogen and the Spectroscopic transitions responsible for them? I could not find them. Please give more details.

Regards,

Rajat

Thanks Eugene for your candid reply. But there are people like Hans who know the details it seems.

Regards,

Rajat

Rajat:

These are not dipole transitions but scattering due to the polarizability of the molecules. A fairly simple discussion is given by Young (1982), a bit more math and details by Bates (1984). An excellent review of atmospheric scattering by molecules and particles can be found in Hansen and Travis (1974). Our group has recently given a simple derivation of lambda^-4 and looked at scattering from small particles (Moosmuller and Arnott (2009) and at blue sunsets on Mars (Ehlers et al., 2014). Have a look, there is much to be learned.

Hans

Bates, D. R. (1984). Rayleigh Scattering by Air. Planet. Space Sci., 32, 785-790.

Ehlers, K., R. Chakrabarty, and H. Moosmüller (2014). Blue Moons and Martian Sunsets. Appl. Opt., 53, 1808-1819.

Hansen, J. E., and L. D. Travis (1974). Light Scattering in Planetary Atmospheres. Space Sci. Rev., 16, 527-610.

Moosmüller, H., and W. P. Arnott (2009). Particle Optics in the Rayleigh Regime. J. Air & Waste Manage. Assoc., 59, 1028-1031.

Young, A. T. (1982). Rayleigh Scattering. Phys. Today, 35, 42-48.

Rajat,

exists the science: Optics of atmosphere. It has many applications in different fields.

Regards,

Eugene.

Rajat,

The fundamental reason of the blue colour of sky in unpolluted atmosphere is the scattering on fluctuations of density in the gas close to the state of critical opalescence. The detailed discussion of this problem is presented by Smoluchowski in his seminal paper: "Beitrag zur theorie der opaleszenz von gasen im kritischen zustande" which was originally published in the Bull. de l'Acad. des Sciences de Cracovie in 1908. The subject was further discussed by Einstein in his classical paper on critical opalescence published in 1910 in Ann. Phys. vol 33 (the paper by Einstein is easily available after google search with: "Einstein papers on critical opalescence").

Regards,

Janusz

Dear Hans Moosmuller,

Many many thanks for your uploading the relevant references. I shall go through them and find out how these sparsely distributed particles (dust, sulphates etc) other than Nitrogen(~78%) and Oxygen(~20%) could possibly determine the color of sky. They may be scattering blue but the majority contribution has to be from Nitrogen and Nitrogen does not give blue!

Regards

Rajat

Dear Janusz,

Could you explain a little more clearly what the color has to do with opalescence of gases in the atmosphere.

Regards,

Rajat

Dear Rajat,

I have included references to two classical papers by Einstein and Smoluchowski in order to underline the importance of considering the effects of fluctuations of thermodynamic properties of the medium. They should be considered as the illustration of the importance of the distinction between coherent and incoherent scattering. According to all experimental facts the fluctuations of density in the atmosphere are responsible for incoherent scattering which is essential to explain many optical properties including the blue colour of sky in unpolluted air.

Regards,

Janusz

Dear Janusz,

 Probably by fluctuation of density you mean variation in space, not in time. As we move upwards the density does change. Incoherent scattering of course is there. But then incoherence should not lead to a particular color like blue. It should get us back the original white, if Rayleigh scattering were not there.

Regards,

Rajat

Dear Hans Moosmuller,

I went through the references suggested by you. They do throw a lot of light on the subject. But, none of them discusses the importance of :

(1) Solar radiant intensity peaking at Blue

(2) Human cone sensitivity being maximum for Blue

as possible factors involved in the blue appearance.

My position is that 1/lambda^4 would surely lead to a violet sky and not a blue sky.

If (425/700)^4 = 1/ 6 can be the reason for blue preponderance over red, then same logic can be cited for violet over blue. In fact, even any inverse positive power of lambda would do, perhaps. 

Granting that Rayleigh scattering also does have a role, to what extent each of these three factors are responsible for the blueness is surely a matter to be investigated.

Regards,

Rajat

Dear Rajat,

Yes, the scattering in the medium with the spatial fluctuations of

density in the spirit of theories developed by Einstein and

Von Smoluchowski. Their ideas are summarized succinctly in the paper

"Einstein: the classical physicist" by J. S. Rowlinson ( Notes and Records

of the Royal Society, 2005, vol 59, 255-271) which is freely available

on the web after the simple Google search.

The concept of including fluctuating properties of the medium is

crucial because the classical Rayleigh theory is formulated for the

medium with very low density in which the scattering centers are

separated by large distances. We know that this assumption is not satisfied

even in the high atmosphere.

When we look closer at the problem of explaining the blue color of sky

it is becoming evident that we should include contributions of Rayleigh,

Von Smoluchowski, Einstein and finally Zimm. Nice discussion of the subject

is presented at the site:

http://www.osti.gov/accomplishments/nuggets/einstein/daytimea.html

In addition to all complexities of the scattering in the medium with the

fluctuating properties I agree also with your remarks concerning the specific

response characteristics of the human eye as the important factor in the

discussion.

With my Best Regards,

Janusz

Thank you very much Dear Janusz.

Let's wait for what Moosmuller has to say on my suggestion.

Blueness requires all three causes.

(1) Solar radiance peaking at Blue.

(2) Human cone sensitivity being maximum for Blue.

(3) Rayleigh Scattering favoring smaller wavelengths. Of course we can add other contributions from Somolouchowski, Einstein and others.

Of these I think the third one is rather a weak cause since it implies violet saky not blue, unless aided by the other two.

Text book explanation is hopelessly inadequate here. They should be rewritten and the real scientific causes discussed.

Regards,

Rajat

Dear Rajat:

Great discussion, I'm working on a contribution but my day job has kept me too busy this week. I hope to post something on the weekend.

Cheers,

Hans

Dear Rajat,

I agree with your opinion. After checking many references in the field of atmospheric optics it is becoming evident that more attention should be paid to describe precisely

light scattering in the atmosphere. More research is also needed to create

better understanding of the biophysical aspects of vision. This work could include

perception of polarization of scattered light. Very interesting paper on this

subject was published recently in the Vision Research. The reference is: Le Floch et al.

(2010), "The polarization sense in human vision", Vision Research vol 50, pp 2048-2054.

The methodology outlined in this paper could be also used to verify other concepts

related to our perceptions of color.

Regards,

Janusz

Thank you very much Janusz.

Interestingly, even if if violet intensity were equal to blue intensity in the scattered light, we would see blue sky, because of cone sensitivity. Up to what value of the ratio of violet to blue intensity  will we see blue and beyond that violet, in spite of higher cone sensitivity for blue.

Regards,

Rajat

It's interesting to quantify this by using the CIE color matching functions to calculate the chromaticity of the Rayleigh Blue sky. This works out to about x,y = 0.23,0.23. However when we do this and render the blue sky on a laptop computer it doesn't quite seem to match what I (and at least one other researcher) perceives. The rendering looks more aqua colored than the reality on a day free of haze. The question becomes whether the CIE approach is accurate for this color spectrum that has lots of blue and violet light. I am planning to recalculate this with a more realistic solar spectrum to see if it helps.