# *Where* does sunlight scattering occur?

Gold Member
I observed a strange phenomenon the other day which led me to ask this question.

I was in Bahamas on a cruise, where it is very bright. This might have enhanced an otherwise more subtle effect.

(OK, get the drinking jokes out of your system now... :tongue:)

I was outside, right next to the hull of the ship on a tender. It was about 11AM, so sun was very high in a virtually cloudless sky. Yet I was so close to a 12 story structure that I was in shadow. It was clear and there was no haze.

I looked up at the sky directly above me, so I was looking through sky that was in ship-shadow into cloudless sky. The sky directly above me was so dark that I thought for a good minute that the sky was completely overcast and grey with cloud cover, like it was about to rain very heavily. Anywhere else I looked the sky was bright, saturated blue, but right above the ship it was this medium foreboding grey.

I'm pretty familiar with sky and weather phenomena, so I have a lot to compare to, but this was odd. It took me a few moments of analysis, and some small clouds to drift into the grey before I could convince myself that the sky I was seeing was actually clear as a bell like everywhere else, and not overcast.

Obviously what was happening was that I was looking at the shadow of the ship. But shadows are a lack of light, which means I should have been looking through dark at bright sky beyond. In a clear hazeless sky, I should not be able to see an absence of light.

It leads me to wonder if most of the scattering due to sunlight actually occurs very near the observer, not across the entire expanse of sky. In a sense, the implication of this is that most the brightness and blueness of a sky is actually being generated less than a 50 metres from the observer.

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## Answers and Replies

My ad hoc theory:
Blue light of the sky has an intensity proportional to $\sin^2\phi/\cos\theta$ where $\phi$ is an angle between your sight axis and the line pointing to the Sun and $\theta$ is an angle between sight axis and Zenith.
It is strongest when you look perpendicular to the line to Sun, low above horizon.
As you were in tropics looking vertically and the Sun was almost in zenith, you got the smallest possible amount of blue light of all conditions.

$\sin^2\phi$ - due to scattering dipolar profile

$1/\cos\theta$ - due to amount of air on your sight path

gray (rather than black) may come from scattering on large particles (dust, etc) in lower parts of atmosphere

It leads me to wonder if most of the scattering due to sunlight actually occurs very near the observer, not across the entire expanse of sky. In a sense, the implication of this is that most the brightness and blueness of a sky is actually being generated less than a 50 metres from the observer.
That can't be true. If it would be, you would see blue light from perpendicular beams of white light: e.g. car lamps.

Or... maybe I was wrong argumenting for $\sin^2\phi$ factor? I must rethink it... Anyway $1/\cos\theta$ seems to be obvious.

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Gold Member
Just one point: blue light of the sky has an intensity proportional to $sin^2\phi/cos\theta$ where $\phi$ is an angle between your sight axis and the line pointing to the Sun and $\theta$ is an angle between sight axis and Zenith.
It is strongest when you look perpendicular to the line to Sun, low above horizon.
As you were in tropics looking vertically and the Sun was almost in zenith, you got the smallest possible amount of blue light of all conditions.

$sin^2\phi$ - due to scattering dipolar profile

$1/cos\theta$ - due to amount of air on your sight path

Yes, I am well aware of this phenom, as an artist, a photographer, a sailor and a weather enthusiast. You can see in my diagram that I've shown the sky blue near the horizon and whiter higher up.

This was distinctly different. It was darker, not lighter. And grey, not blue or white.

Gold Member
That can't be true. If it would be, you would see blue light from perpendicular beams of white light: e.g. car lamps.

I see your point, though I am not sure the two scenarios are equivalent. Many factors between them are different.

Photographer? So where are the photos? Of course - made with polarized filter...

Gold Member
Photographer? So where are the photos? Of course - made with polarized filter...

I considered taking some photos, but there was no way I could. I would have needed a fish-eye lens on my point-n-shoot. The phenom needed the whole sky to be seen, and that's a lot of PhotoShop stitching...

I must admit - I was totally wrong. Wiki says that blue sky comes from Rayleigh scattering - which intensity is even stronger along the axis than perpendicular. So we have $$\frac{1+\cos^2\phi}{\cos\theta}$$
I am confused - I see no explanation for your phenomenon then... I never saw that, but I've never been sailing on tropical waters...

A.T.
I don't need to tell you that human visual perception is highly subjective. The eye & brain are correcting the perceived luminosity and tint. Just because a part of the sky looked darker, doesn't mean it was darker. It might have looked darker in contrast to the white(?) ship hull. Just because the sky looked less saturated(blue), doesn't mean it was. The brain normalizes colors.

As for objective effects: A clear sky can be darker right above, because you look trough less atmosphere and thus see less scattered light.

sophiecentaur
Gold Member
2020 Award
A.T. is probably pretty near the mark. As I was reading this thread the phrase "integrating to grey" kept coming to mind. If the sun is overhead than, as you all agree, there will be a very blue blue on the periphery - bluer than your brain expects. So the not-so-blue bits will look much less saturated (i.e. greyish).

One has to remember that the bluest blue sky and the reddest sunset are not very saturated colours - just stronger than we're used to. They're only bluish and reddish.

Wouldn't this be the same phenomenon as standing in a well during the day and seeing the stars?

Gold Member
Yeah, as I said, I'm pretty perceptive of these kinds of things. While I can't refute the idea that it was a subjective, experiential thing, I plan to keep soliciting for physical explanations.

sophiecentaur
Gold Member
2020 Award
Wouldn't this be the same phenomenon as standing in a well during the day and seeing the stars?

Is there any evidence that you can actually see stars this way?

A.T.
Wouldn't this be the same phenomenon as standing in a well during the day and seeing the stars?

Does this work? It doesn't according to this:
http://www.snopes.com/science/well.asp
But this is again about human perception.

To have an objective measure you would need to take two pictures with exactly the same camera settings from the surface and from the well. For the surface picture you could restrict the field of view with a blend right in front of the camera, so that you see the same amount of sky. Or use a strong zoom, such that you don't see the well walls, and the same zoom at the surface.

Then you would compare the brightness of the sky in the two pictures. You could of course use some light sensor directly to measure the intensity.

sophiecentaur
Gold Member
2020 Award
I might suggest that the reason for some of this effect could be the existence of flare inside your actual eye. They are far from perfect optics - relying on a lot of image processing to get the high standard of imaging that the luckiest of us are blessed with. (Eat yer heart out Legolas) Everyone who uses a camera seriously knows about using a lens hood, even in. circs where you might not think it necessary. Under nearly all conditions, we see the sky, modified by a lot of natural flare and 'bluer' than it really is.

I think Dave's observation was there because of the lens hood, in the shape of the ship and, because this phenomenon is so rarely revealed, it appeared very extreme. The brain is very funny about some things.
I looked for some evidence. Looking through a lot of pictures in my Aperture Library, I see that the bluest of blue skies (not Caribbean) have typical values of R56, G75, B117, which shows how unsaturated a 'really blue sky' blue is. I also looked at 'really red' sunsets, finding typical values of R193, G90, B38. Also, by hunting around in areas of sunset pictures, it was very easy to find pretty much equal values of RGB (grey!!).
So, it is possible to find areas of sky, in many pictures, which are actually grey - when there is an appropriate scattering away of some wavelengths and scattering towards of some others.

The only way, Dave, to be sure is to go and have another holiday and take the camera with a fisheye lens and other lenses - making sure to put the exposure on manual.

Boy, what an excuse!

Have you ever looked up at the sky from inside an airplane window at high altitude? I have and I think it looks more white than blue lending credence to your feeling that scattering occurs closer to the surface. There is another fact indicating your feeling is correct. The atmosphere is thicker near the surface and has more dust particles increasing the likelyhood of scattering.

Here's 2 questions, where you wearing appropriately shaped optics? (Prescription eyeglasses) and what color are your eyes?

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Polarised sunglasses + polarisation of diffuse sky radiation could lead to the perception of dark regions.

sophiecentaur
Gold Member
2020 Award
Aeroplane windows could be responsible for some of the effect. They are not good, optically (they don't need to be) and are made of plastic which will be abraded and become slightly 'frosted' over time.
If there were appreciably less scattering at this height then why would you expect to see "white"? If there were no scattering then you would just see into space without any scattered sunlight . The blue sky actually gets darker and darker (not more saturated blue) as you go up. The proportion of blue vs red light would be much the same, at any given angle.
It's quite hard to look up out of a plane window so I have no idea what it looks like. I must remember to look next time. I think you are mostly looking out horizontally.
As you get higher, the horizon gets further away. Some of the extra scattered blue light that you see has originated at a greater distance. This light then has to travel through a greater distance and, just as with a sunset, there will be a 'reddening' of what you see because the blue is scattered away again. Although not a lot, this will go towards reducing the saturation of the blue that you see - making the horizon appear whiter. Light coming in vertically only passes through, perhaps 100km of air (most of it pretty rarified) Light which is skimming the atmosphere from the horizon can be passing through many hundreds of km of relatively dense air.

It's quite hard to look up out of a plane window so I have no idea what it looks like. I must remember to look next time.
I am 185cm tall too ;) but airplanes sometimes turn - even at high altitudes they slant by 30deg or more. At 35,000 feet you may spot brightest stars when the Sun is low above horizon.

sophiecentaur
Gold Member
2020 Award
Turning . . . . good idea.

Aeroplane windows could be responsible for some of the effect. They are not good, optically (they don't need to be) and are made of plastic which will be abraded and become slightly 'frosted' over time.
If there were appreciably less scattering at this height then why would you expect to see "white"? If there were no scattering then you would just see into space without any scattered sunlight . The blue sky actually gets darker and darker (not more saturated blue) as you go up. The proportion of blue vs red light would be much the same, at any given angle.
It's quite hard to look up out of a plane window so I have no idea what it looks like. I must remember to look next time. I think you are mostly looking out horizontally.
As you get higher, the horizon gets further away. Some of the extra scattered blue light that you see has originated at a greater distance. This light then has to travel through a greater distance and, just as with a sunset, there will be a 'reddening' of what you see because the blue is scattered away again. Although not a lot, this will go towards reducing the saturation of the blue that you see - making the horizon appear whiter. Light coming in vertically only passes through, perhaps 100km of air (most of it pretty rarified) Light which is skimming the atmosphere from the horizon can be passing through many hundreds of km of relatively dense air.

Well, it wasn't white like printer paper. As i remember it, it was more like a dull white, sort of grey, but definitely not blue. If all scattering is equal at high altitude (20000 ft) even if the scattering is diminished, then the overall impression may be of a whitish, greyish hue. Depends on how close to the sun you look.

Of course the higher you go, the less scattering so the sky should get darker and darker.

Notice the color of the sun in this skydiving video, not yellow, is it? Notice the color of the sky in the near vicinity of the sun, not blue is it?

Heres a jump from 30 km. The sun is so white, i have never seen white like this on earth.

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Gold Member
Notice the color of the sun in this skydiving video, not yellow, is it? Notice the color of the sky in the near vicinity of the sun, not blue is it?

Heres a jump from 30 km. The sun is so white, i have never seen white like this on earth.

There is no such thing as true colour in video or photography. The only way to assess the colour would be to employ a colour calibrating card in the shot.

There is no such thing as true colour in video or photography. The only way to assess the colour would be to employ a colour calibrating card in the shot.

If I were to ask an astronaut (Dave Bowman) to describe the color of the sun from space, what would he say?

Are you saying all colors in photographs and videos are not to be trusted? Dave...?

sophiecentaur
Gold Member
2020 Award
Well, it wasn't white like printer paper. As i remember it, it was more like a dull white, sort of grey, but definitely not blue. If all scattering is equal at high altitude (20000 ft) even if the scattering is diminished, then the overall impression may be of a whitish, greyish hue. Depends on how close to the sun you look.

Of course the higher you go, the less scattering so the sky should get darker and darker.

Notice the color of the sun in this skydiving video, not yellow, is it? Notice the color of the sky in the near vicinity of the sun, not blue is it?

Heres a jump from 30 km. The sun is so white, i have never seen white like this on earth.

I guess that, amongst all the other things the sky divers were having to think about, they would not have remembered to set the colour balance to anything in particular nor to put a strong neutral density filter in front of the lens for accurate colourimetric measurement of the Sun's image. It would have been Point-and-Shoot and grossly overexposed at times, I'm sure. This, for electronic sensors, would drive them into limiting so all information would be lost. Not real evidence of anything really.

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I guess that, amongst all the other things the sky divers were having to think about, they would not have remembered to set the colour balance to anything in particular nor to put a strong neutral density filter in front of the lens for accurate colourimetric measurement of the Sun's image. It would have been Point-and-Shoot and grossly overexposed at times, I'm sure. This, for electronic sensors, would drive them into limiting so all information would be lost. Not real evidence of anything really.

http://www.universetoday.com/18689/color-of-the-sun/

sophiecentaur