Why is the Sky Blue?

To understand why the sky is blue, we need to consider the nature of sunlight and how it interacts with the gas molecules that make up our atmosphere. Sunlight, which is white to the human eye, is a mixture of all the colours of the rainbow. For many purposes, sunlight can be thought of as an electromagnetic wave. When sunlight passes through the atmosphere, it causes the charged particles (electrons and protons) in the air molecules to oscillate up and down. When this happens, the oscillating charge will produce electromagnetic radiation with the same frequency as the incident sunlight but will spread in all different directions. This redirection of air molecules to incident sunlight is called scattering.

The blue component in the visible light spectrum has a shorter wavelength and a higher frequency than the red component. Therefore, when the sunlight of all colours passes through the air, the blue part causes the charged particles to oscillate faster than the red part. The faster the oscillation, the more scattered light is generated, so blue is scattered more strongly than red. For particles such as air molecules that are much smaller than the wavelength of visible light, the difference is huge. The acceleration of a charged particle is proportional to the square of the frequency, and the intensity of the scattered light is proportional to the square of the acceleration. Therefore, the intensity of scattered light is proportional to the fourth power of the frequency. The result is that the efficiency of blue light scattering to other directions is almost 10 times that of red light.

When we observe any point in the sky far away from the sun, we can only see the light redirected into our line of sight by the atmosphere. Because this happens more often with blue light than red light, the sky looks blue. The scattering of violet light is actually stronger than that of blue. 
However, the sunlight entering the atmosphere is more blue than purple, and our eyes are more sensitive to blue light than purple light, so the sky looks blue.
When we see the sunset on the horizon, the situation is just the opposite. We only see the light that is not scattered in other directions. The red-wavelength sunlight that passes through the atmosphere without being scattered reaches our eyes, while the strongly scattered blue light does not. The longer the sunlight travels through the atmosphere on the horizon, the effect will be magnified compared to when the sun is overhead, there is more opportunity for the blue light to scatter. Therefore, the sunset looks reddish. In a polluted sky, small aerosol particles of sulfate, organic carbon, or mineral dust further amplify the scattering of blue light, making sunsets under polluted conditions sometimes spectacular.

On the other hand, clouds are made up of water droplets whose wavelengths are much larger than that of visible light. They scatter sunlight depending on how the light is refracted, internally reflected, and diffracted by cloud droplets. The difference between blue and red light scattering is far less than that of gas molecules for these particles. Therefore, our eyes receive a large amount of scattered light of all visible wavelengths, causing clouds to look whiter than blue, especially when viewed against a blue sky background.
The sky is blue due to atmospheric scattering, so a planet without an atmosphere cannot have a bright sky. For example, photos taken by Apollo astronauts on the moon show that the surface of the moon is bathed in sunlight, but in all directions away from the sun is a dark sky.

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