Of course we all know why the sky is blue. It's because molecules in our atmosphere scatter shorter wavelength light (blue) more strongly than longer wavelength light (red)... right? WRONG!! For, if that was indeed the whole story, the sky should be purple rather than blue.
There is not a problem with the physics involved in the classic explanation. Electromagnetic theory does indeed say that for small particles, such as those in our atmosphere, the intensity of scattered light is proportional to the frequency of incoming light to the fourth power (or the wavelength to the negative fourth power). Thus the intensity of scattered blue light of wavelength 500nm is about 3x that of scattered red light of wavelength 700nm.
So far so good, however, the visible spectrum doesn't end with blue!!! Our eyes are able to pick up on wavelengths shorter than blue - namely purple. Thus, if the intensity of scattered light is the whole story, we should expect a purple sky rather than a blue one. Hmmm...
There are two simple explanations for why the sky we see is blue not purple. The first is that the incoming sunlight hitting the sky is more blue than purple. This basically means that even though purple light is scattered more strongly than blue light, there is much more blue light hitting our atmosphere in the first place than purple. The second option, which I find slightly more exciting, is that the response of our eye has an inherent color bias, which would imply that the visible sky really is purple, and we only perceive it as blue.
The former idea - that the solar spectrum has something to do with it - is more familiar territory to me than the latter, so I will examine that first. We can approximate the sun as a blackbody and use Planck's Law to determine the number of photons emitted at each wavelength per unit time. Since these photons are what actually hits the atmosphere, we can multiply this number by the scattering intensity at that wavelength to recover the net intensity per unit time as a function of wavelength.
The result of this correction is shown below. As you can see, the Solar spectrum actually does peak in the green, which, at first, makes me think: "OK green sun + purple scattering = blue skies". Unfortunately, the correction is not quite strong enough to explain the blue sky. As the plot shows, the total sky intensity still peaks at the shortest possible visible wavelength (i.e. purple at 400 nm).
There is not a problem with the physics involved in the classic explanation. Electromagnetic theory does indeed say that for small particles, such as those in our atmosphere, the intensity of scattered light is proportional to the frequency of incoming light to the fourth power (or the wavelength to the negative fourth power). Thus the intensity of scattered blue light of wavelength 500nm is about 3x that of scattered red light of wavelength 700nm.
So far so good, however, the visible spectrum doesn't end with blue!!! Our eyes are able to pick up on wavelengths shorter than blue - namely purple. Thus, if the intensity of scattered light is the whole story, we should expect a purple sky rather than a blue one. Hmmm...
There are two simple explanations for why the sky we see is blue not purple. The first is that the incoming sunlight hitting the sky is more blue than purple. This basically means that even though purple light is scattered more strongly than blue light, there is much more blue light hitting our atmosphere in the first place than purple. The second option, which I find slightly more exciting, is that the response of our eye has an inherent color bias, which would imply that the visible sky really is purple, and we only perceive it as blue.
The former idea - that the solar spectrum has something to do with it - is more familiar territory to me than the latter, so I will examine that first. We can approximate the sun as a blackbody and use Planck's Law to determine the number of photons emitted at each wavelength per unit time. Since these photons are what actually hits the atmosphere, we can multiply this number by the scattering intensity at that wavelength to recover the net intensity per unit time as a function of wavelength.
The result of this correction is shown below. As you can see, the Solar spectrum actually does peak in the green, which, at first, makes me think: "OK green sun + purple scattering = blue skies". Unfortunately, the correction is not quite strong enough to explain the blue sky. As the plot shows, the total sky intensity still peaks at the shortest possible visible wavelength (i.e. purple at 400 nm).
This implies that visible sky really is brighter in purple (and shorter wavelengths) and it is our eyes/brain that make it look blue.
What we would need to show this is some sort of experiment demonstrating the response function of our eye to different visible colors. For CCDs used by telescopes as detectors, this experiment is called the Quantum Efficiency, and it gives the probability of a given color photon being picked up by the detector. If we could get the something analogous to the Quantum Efficiency for human eyes, then we would just add this correction to the plot above to determine what intensity the sun+sky+eyes system peaks at. If this theory is correct, the color must peak somewhere in around sky blue.
Fortunately, such a plot exists in a chapter of Fred Schubert's book Light Emitting Diodes:
What we would need to show this is some sort of experiment demonstrating the response function of our eye to different visible colors. For CCDs used by telescopes as detectors, this experiment is called the Quantum Efficiency, and it gives the probability of a given color photon being picked up by the detector. If we could get the something analogous to the Quantum Efficiency for human eyes, then we would just add this correction to the plot above to determine what intensity the sun+sky+eyes system peaks at. If this theory is correct, the color must peak somewhere in around sky blue.
Fortunately, such a plot exists in a chapter of Fred Schubert's book Light Emitting Diodes:
The above plot is the "Quantum Efficiency of the Human Eye" that we are looking for and shows our eyes are twice as sensitive to blue light than they are to purple light! We can roughly interpret this as our eyes detecting two blue photons to every one purple photon assuming blue and purple photons are emitted equally. This factor of two is more than enough to see the sky as blue rather than purple, since the difference between the number of purple and blue photons being emitted by the sky is only about 20% (Figure 1).
Thus, even though the sky is emitting more purple photons, our eyes pick up more blue light and therefore see the sky as blue!
The crazy thing about this is that this response function is that it is specific to humans. Granted, there are evolutionary reasons why one might expect humans to see frequencies in this way, but I am reasonably confident that other animals will have other solutions to this problem. Therefore, the color of the sky depends on the animal you ask... humans see the sky as blue, bees see the sky as ultraviolet, and I think rhinos are basically blind...
Thus, even though the sky is emitting more purple photons, our eyes pick up more blue light and therefore see the sky as blue!
The crazy thing about this is that this response function is that it is specific to humans. Granted, there are evolutionary reasons why one might expect humans to see frequencies in this way, but I am reasonably confident that other animals will have other solutions to this problem. Therefore, the color of the sky depends on the animal you ask... humans see the sky as blue, bees see the sky as ultraviolet, and I think rhinos are basically blind...