Why is the sky blue? — Clear physics explanation for a 24-year-old (Rayleigh scattering, wavelength dependence, and sunsets)

Quick answer

The sky looks blue because air molecules scatter shorter (bluer) wavelengths of sunlight much more strongly than longer (redder) wavelengths. That selective scattering sends more blue light toward your eyes from all directions.

Step-by-step explanation

1. Sunlight contains all visible colors.

   Sunlight is basically white light, a mix of many wavelengths (colors) from violet (~380 nm) through red (~740 nm).

2. The atmosphere is full of tiny particles (molecules).

   Air is mostly nitrogen and oxygen molecules, which are much smaller than the wavelengths of visible light.

3. Small particles cause Rayleigh scattering.

   When particles are much smaller than the wavelength of light, scattering follows Rayleigh's law: the scattered intensity is proportional to 1/λ^4. In plain terms, shorter wavelengths (blue and violet) are scattered far more strongly than long wavelengths (red).

   So blue light (around 450 nm) is scattered several times more than red light (around 650 nm). For example, (650/450)^4 ≈ 4.3, meaning blue is scattered roughly four times more than red in that comparison.

4. More scattered blue light reaches your eyes from every direction.

   Because the scattered blue photons come to you from many directions in the sky, the large part of the dome above you appears blue instead of the direct white color of the Sun.

5. Why not violet, if violet scatters even more?
   • Sunlight contains less violet than blue.
   • Human eyes are less sensitive to violet (our cone cells respond strongest in the blue-green region).
   • Some violet is absorbed higher in the atmosphere (for example by ozone).

   All these factors combine so our brains perceive the scattered light as blue rather than violet.

6. Why sunsets are red/orange.

   When the Sun is near the horizon, sunlight travels through a much longer path in the atmosphere. Most of the shorter wavelengths (blue and green) get scattered out long before the light reaches your eye. The remaining direct light is dominated by longer wavelengths (red and orange), so the Sun and the sky near the horizon look reddish.

7. What about white clouds and hazy skies?

   Cloud droplets and larger particles scatter light by Mie scattering, which depends much less on wavelength, so they scatter all colors about equally. That produces white or gray clouds and whitish haze.

Short wrap-up

Daytime sky = blue because small air molecules scatter shorter wavelengths (blue) far more strongly than red (Rayleigh scattering, ~1/λ^4). Sunsets = red because the long path removes most blue light. Larger particles (aerosols, droplets) scatter all colors more equally (Mie scattering), which is why clouds look white.

Helpful one-line formula

Scattered intensity ∝ 1/λ^4 (Rayleigh scattering) — shorter wavelengths are scattered much more.