Why is the Sky Blue?

Schematic animation of a continuous beam of light being dispersed by a prism. The white beam represents many wavelengths of visible light, of which 7 are shown, as they travel through a vacuum with equal speeds c. The prism causes the light to slow down, which bends its path by the process of refraction. This effect occurs more strongly in the shorter wavelengths (violet end) than in the longer wavelengths (red end), thereby dispersing the constituents. As exiting the prism, each component returns to the same original speed and is refracted again.
Light Dispersion Conceptual Waves by
Lucas V. Barbosa. 2007.

Some Background

In the image above, a beam of light passes through a medium. The medium slows down the light and causes it to refract. And the degree of refraction is dependent on the wavelength of light: shorter wavelength light will slow down more and therefore have a greater angle of refraction. See Cauchy’s equation below for the inverse relationship between refractive index and wavelength of light in a transparent medium.

  B + \frac{C}{\gamma^{2}}

Our Sun emits a continuous spectrum of light, called black body radiation, which is predictable by its temperature. For the purposes of clarity, we will assume that the Sun emits all the visible wavelengths of light and they reach Earth’s atmosphere.

Why does the sky appear blue?

The shorter wavelength blue light scatters in Earth’s atmosphere more than the longer wavelength red light. Thus, the sky appears blue. And when the Sun’s light travels a long distance to reach us, such as during a sunrise or a sunset, the sky will appear yellow, orange, or red. This phenomenon also explains why a lunar eclipse appears reddish in color, since red light scatters the least as Earth reflects light into space.

Since violet is the shortest wavelength, the sky should appear violet, right?

The sky does appear violet… but not to humans.

The human eye uses three different types of cones to view color. About 64% of these cones are sensitive to red light, about 32% are sensitive to green light, and about 2% are sensitive to blue light. The sensitivity of the cones tend to be similar, despite the disparity of blue cones.

Simplified human cone response curves. Curves show blue, green, and red sensitivities.
Simplified human cones response curve. based on Dicklyon, which is based on Stockman, MacLeon and Johnson. by Vanessaezekowitz. 2007

When the light from the atmosphere reaches our eyes, the blue-sensitive cones are stimulated the most, with a small amount of stimulation to the green- and red-sensitive cones. This mixed hue actually creates the same cone response as “pure” blue and white light.

In the same vein, animals have varied abilities to see color. Many animals only have two cones instead of three. And some animals can see wavelengths invisible to humans. For instance, the honeybee can see ultraviolet light and discerns UV patterns on flowers, which facilitates gathering nectar.