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#1 2007-11-22 01:03:02

sinaptix
Member
Registered: 2005-07-09

Why are sunsets red?

...and why is the sky blue?

http://stochastix.wordpress.com/2007/02 … t-physics/

There are some mathematical characters so it's better to click the link above and read the article from the original site. The text quoted below is more messy and it might not make as much sense. (edit: fixing link up)

Sunset Physics

We’ve all seen the Sun setting and the twilight slowly arriving. It’s a sight to behold! Over many centuries, sunsets have inspired poets, writers, painters, and “beauty-sensitive” average citizens.

newport-beach-at-sunset.jpg

[ a beautiful sunset at Newport Beach, Orange County, California - Photo courtesy of Mike Liebner from Creative Power ]

At a very tender age, I started to come up with rather deeps questions such as “why is the sky blue?”, which led me to think of another question: “why does the sky look reddish at sunset?”. I assume that the reader has wondered about the very same issues at some point of his/her life. We know that the sky is blue during the day, and that it gets reddish at sunset. Those are unquestionable facts. But why is that so? What are the underlying physical principles that explain this phenomenon?

Allow me to dwell on this…

The Sun emits light and other electromagnetic (EM) radiation, such as infrared (IR), ultra-violet (UV), X-rays, among other types of radiation. The Human eye can “see” only in a very narrow wavelength band of the EM spectrum, ranging from about 400 to about 700 nanometers. The fact that Humans can only “see” in this narrow wavelength band is, in a way, a coincidence. It just happened to be so. Other animals can “see” in different wavelength bands of the EM spectrum: night predators, for instance, can often “see” in the infrared (IR) range, which means that Nature equipped them with night-vision goggles, so to speak!

The EM radiation emitted by the Sun travels undisturbed through the void of outer space for millions and millions of miles, until it reaches the Earth’s atmosphere and starts interacting with the molecules that constitute the atmosphere (such as oxygen, nitrogen, carbon dioxide, etc). UV light and lower wavelength (higher frequency) radiation carry enough energy to ionize the molecules in the outer layers of the atmosphere. This causes energy to be transfered from the EM field to the medium with which the radiation is interacting. Visible light does not carry enough energy to ionize the atmosphere’s molecules, and thus it “passes through” the atmosphere pretty much undisturbed, transferring relatively little energy to the medium. This means that most visible light gets to the innermost layers of the atmosphere (close to the Earth’s surface), while higher energy radiation is transferred to the medium (i.e., absorbed) in the outer layers of the atmosphere. Fortunately, the Earth’s atmosphere blocks most of the high-energy ionizing radiation which is known to cause cancer.

However, not all visible radiation propagates the same way through the atmosphere! Due to a physical phenomena called Rayleigh Scattering, we have that the light scattering is proportional to \lambda^{-4}, where \lambda is the radiation’s wavelenght. Blue light has a lower wavelength (higher frequency) than red light, the ratio between the two wavelengths being approximately 1.75. This means that blue light is scattered 1.75^4 \approx 10 times more intensely than red light.

Imagine that you are looking at the Sun, and let us think of the light that gets to our eyes, and the light that is scattered to the whole sky. Let us also assume that the Sun emits the same power of red and blue light. Then, we have that red light will get to your eyes (though it suffers scattering), and the Sun will look more reddish than blue. Ok, but where’s the blue light!?

The blue light is everywhere in the sky! :-)

Given that blue light is scattered approximately 10 times more intensely than red light, the sky will be 10 times more blue than red (so to speak)! Note that if there were no atmosphere, the sky would look as black as outer space. When we look at the sky, what we see is blue light being scattered all around, ando this is possible only because there are molecules in the air which emit blue light. Photons are thus “random walking” all over the sky, jumping from atom to atom, causing the atoms’ electrons to jump to excited states, and then decaying back to the ground state. Due to Rayleight Scattering, there are many more “blue photons” in the sky than “red photons”. As a result, the sky is blue! It’s not magic, it’s Physics…

OK, this sounds great! But what about the sunset!? Why does the sky look reddish at sunset?

That is a geometric phenomenon! When the Sun is at the zenith, the EM radiation emitted by the Sun will have to travel through approximately h = 80 Km of atmosphere. However, at sunset, the Sun is close to the horizon and light will have to travel through a much greater distance! Let \theta be the angle of the sun, measured from the zenith, then when the Sun is at the zenith, we have \theta = 0, and when the Sun is at the horizon, we have \theta = \pi / 2. When the Sun is not at the zenith, it will have to travel a distance d = h \sec(\theta), where \sec(\theta) = 1 / \cos(\theta) > 1, \forall \theta \in (0, \pi/2].

Given that the light will have will have to travel a much higher distance when the Sun is closer to the horizon, then the Rayleigh Scattering will also be much higher, and the red light will now be much more scattered to the sky. Thus, the sky will look reddish. Given that there will be less blue light in the spot where we see the Sun, the Sun will also look reddish. At noon, there will be much more blue light in the spot where the Sun is, and thus the Sun will look whiter.

Last edited by sinaptix (2007-11-22 01:04:34)

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#2 2007-11-22 02:28:39

sinaptix
Member
Registered: 2005-07-09

Re: Why are sunsets red?

This is totally unrelated but I don't know where to put it, found it on the same blog, cool little story:

Once upon a time, a king carried by his slaves wanted to cross a rope bridge. He called all his slaves and asked, "Is it safe? Someone go ahead and cross."

All but one stared at each other and began to point and say, "Your excellency, send him, he is wisest and can tell you if it is safe." Each poor slave pointed at another, and another. Finally, one said, "Let me go across, sire."

Having crossed the bridge, he cut the rope.

Source

Last edited by sinaptix (2007-11-22 02:29:05)

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#3 2007-11-22 16:23:15

DanB
Member
Registered: 2007-06-05

Re: Why are sunsets red?

Hi Sinaptix,

Thought I'd post that beautiful pic from Your start-up post:

http://stochastix.files.wordpress.com/2007/02/newport-beach-at-sunset.jpg

I'm kinda "partial" to the sun and it's beauty...if You check some of my posts here : )

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#4 2007-11-22 17:48:19

sinaptix
Member
Registered: 2005-07-09

Re: Why are sunsets red?

Hi DanB,

Yah definitely I've seen your posts and have followed sun-gazing with a lot of interest. I don't post a lot but I do stop by NR daily for years now. I keep falling off the sun-gazing wagon though. I've been trying on and off for a few years now, gotten up to a couple minutes a few times.

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#5 2008-01-27 02:38:13

persephonevii
Member
Registered: 2007-06-28

Re: Why are sunsets red?

Sometimes I see sunsets so beautiful I just think they can't be real, someone must of painted them. Like that picture above, so beautiful and dreamy... it's hard to imagine splitting light can create such an image. Sunrises are great too. Also the light at sunset and sunrise gives the land a strange ethereal quality at times. The world seems to be almost a different place at those times.

Sinaptix I liked your king crossing the bridge story. I'd do that too if I were his slave!

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#6 2008-01-27 04:03:13

Spi
arcane adventurer
Registered: 2007-10-18

Re: Why are sunsets red?

http://img242.imageshack.us/img242/883/sunriseap6.png


Last edited by Spi (2008-01-27 04:08:19)

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