# Why is the sky blue?

Category: Earth Science
Published: March 28, 2013

Announcement!
Dr. Baird's book is now available:
The Top 50 Science Questions

If you look in any popular science book on this topic, it will tell you that the sky is blue because of Rayleigh scattering in the atmosphere. While Rayleigh scattering is a very important part of the answer, it is not the only part. If the only effect at work were Rayleigh scattering, then the sky would be violet, not blue. In fact, there are four factors involved; all required to give the final answer of blue:

• Rayleigh scattering in the atmosphere
• The incident sunlight spectrum is a thermal distribution
• Bulk attenuation by the atmosphere
• The human eyes and brain mix and perceive colors non-linearly

Rayleigh scattering is what happens when light bounces off an object that is much smaller than its wavelength. Physical derivations show that for Rayleigh scattering, the higher frequency colors such as blue and violet are scattered much more strongly than low frequency colors such as red and orange. Mathematically, the intensity of scattered light is proportional to f 4, where f is the frequency of the light. This means that a color that is twice the frequency of another color will be 16 times brighter than that other color after scattering if they both were equally bright to start out with. In the atmosphere, the objects doing the scattering are mostly nitrogen molecules (N2) and oxygen molecules (O2). These molecules are much smaller than visible light (oxygen molecules are about 0.1 nanometers wide and visible light has a wavelength of about 500 nanometers), so the scattering in the atmosphere is Rayleigh scattering. But if this were the end of the story, the sky would be violet and not blue because violet is the highest-frequency visible color. Let us look at the other effects.

The color spectrum of the sky if only Rayleigh scattering were involved. The sky would look violet. It's a good thing there is more going on than Rayleigh scattering, otherwise we would be fried by all that ultraviolet radiation. The y axis is the brightness of a certain color. Public Domain Image, source: Christopher S. Baird.

Most people think that the sunlight traveling through space before it hits our atmosphere is a perfectly white color. Perfect white is an equal mix of all colors. In reality, the sunlight hitting the atmosphere does not have an equal distribution of colors, but has a thermal (black-body) distribution. The sun is a big ball of incandescent gas very similar to a candle flame. The light that our sun sends out into to space is created by its heat, and therefore it has a thermal distribution of colors. The exact nature of a thermal distribution depends on the temperature of the glowing object (i.e. red-hot toaster elements vs. white-hot coals). The sun's surface temperature is at about 5800 Kelvin, which gives a thermal distribution that peaks in the infrared (in frequency space). The sunlight that hits the atmosphere is therefore not an equal mix of all colors, but is a mix of all colors with red-orange dominating, and with more blue than violet (at least in frequency space). This helps explain why the sky is blue and not violet. But it turns out to still not be enough.

The color spectrum of the sky considering Rayleigh scattering + thermal incident sunlight. Public Domain Image, source: Christopher S. Baird.

Bulk attenuation means that as sunlight travels through the thick atmosphere, it becomes progressively weaker because it is being partially scattered all along the way. The rate at which it becomes weaker is faster for higher-frequency colors. In other words, because blue and violet scatter the strongest, they are also removed the quickest from the forward traveling beam as it travels down through atmosphere. Bulk attenuation is what makes sunsets red and orange. At sunset, the sunlight is approaching an observer at a low angle, so it has to travel through much more atmosphere. It travels through so much air in fact, that by the time the light reaches the layer of air closest to the grounded observer, all of the green, blue and violet colors have long since been scattered out by higher layers of atmosphere, leaving just red and orange. While it is still true that the air in the layer of sky closest to the observer scatters blue and violet light the strongest, there is no blue or violet light left in the light beam to scatter at sunset because of bulk attenuation. Even during the day when the sun is high in the sky, bulk attenuation has an effect. The sunlight in the forward beam near the bottom of the atmosphere has less violet than blue as compared to the beam when it was in the top of the atmosphere because the violet color scatters more quickly our of the forward beam. While this helps explain why the sky is blue and not violet, it is not enough.

The color spectrum of the sky considering Rayleigh scattering + thermal incident sunlight + bulk attenuation around noon near the equator. At sunset, the bulk attenuation effect shifts this entire curve to red colors. Public Domain Image, source: Christopher S. Baird.

Finally, human eyes perceive color in a non-linear fashion. For instance, if a blue spot on the wall sits next to a violet spot on the wall, and a laboratory tool measures them both to be equal brightness, our eyes will perceive the blue spot to be brighter. In a loose sense, our eyes are more sensitive to blue light than violet light. But the situation is more complex than this statement makes it seem. Our eyes have three color receptors: red, green, and blue, but these receptors overlap quite a bit. Our brains then mix the three signals non-linearly to give us the experience of color. In a simplified view, equal parts of red, green, and blue are perceived as white, whereas a little red plus a little green plus a lot of blue-violet is perceived as whitish-blue. Our brains mix together the spectrum shown above to give us the sky blue shown below. All of the effects mentioned above are needed to explain why humans see the sky as blue.

Our eyes and brain combine the spectrum of colors in the previous image to give us this color. Public Domain Image, source: Christopher S. Baird.