Rayleigh scattering

Rayleigh scattering is a fundamental physical phenomenon that explains how light interacts with particles much smaller than its wavelength. Named after the British physicist Lord Rayleigh, who first described it in the 19th century, this process plays a crucial role in understanding remote sensing, atmospheric optics, and various natural phenomena.

Basic Principles

Rayleigh scattering occurs when electromagnetic waves, such as light, are scattered by particles whose size is less than about one-tenth of the wavelength of the light. Unlike other scattering mechanisms, the intensity of Rayleigh scattering is highly wavelength-dependent, varying inversely with the fourth power of the wavelength $(\sim \lambda ^{-}4)$. This means shorter wavelengths (e.g., blue light) are scattered more than longer wavelengths (e.g., red light). For the same incoming intensity, scattering at 400 nm is 9.4 times higher than at 700 nm. Rayleigh scattering of sunlight in Earth's atmosphere creates diffuse sky radiation, which is responsible for the blue colour of the daylight and twilight sky, as well as the yellowish to reddish colour of the low Sun.

Key characteristics:

• Dependence on Particle Size: Effective only for particles much smaller than the wavelength of light, such as air molecules.
• Wavelength Dependence: Explains the blue colour of the sky during the day and the reddish hues of sunsets and sunrises.
• Polarization: Light scattered by Rayleigh scattering is partially polarized, a property utilised in various remote sensing applications.

Physical Explanation

When light passes through a medium containing small particles or molecules, the oscillating electric field of the light wave induces oscillations in the electrons of the particles. These oscillating charges act as secondary sources of light, radiating in all directions. Since smaller particles cannot resonate effectively with longer wavelengths, shorter wavelengths dominate the scattered light.

Mathematical Representation

The intensity of Rayleigh scattering can be expressed as:

$$I_{s}=I_{0}{\frac {1+\cos ^{2}\theta }{2R^{2}}}\left({\frac {2\pi }{\lambda }}\right)^{4}\left({\frac {n^{2}-1}{n^{2}+2}}\right)^{2}r^{6}$$

Averaging this over all angles gives the Rayleigh scattering cross-section of the particles in air:

$$\sigma _{\text{s}}={\frac {8\pi }{3}}\left({\frac {2\pi }{\lambda }}\right)^{4}\left({\frac {n^{2}-1}{n^{2}+2}}\right)^{2}r^{6}$$

Useful Resources

• Rayleigh scattering - Wikipedia
• Blue Sky and Rayleigh Scattering - HyperPhysics