Rayleigh scattering

Rayleigh scattering is the deflection of light or other electromagnetic radiation by particles. These particles must be much smaller than the wavelength of the radiation itself. This phenomenon is responsible for many natural optical effects. It is the primary reason our sky appears blue during the day. It also explains why sunsets appear in shades of red and orange. Understanding this process helps scientists study how light moves through gases, liquids, and solids.

To understand the mechanism, we must look at how light interacts with matter. Light waves have an oscillating electric field. When this field hits a tiny particle, it acts on the charges within that particle. This causes the charges to move at the same frequency as the light. The particle then becomes a small radiating dipole. This means the particle itself sends out new radiation, which we see as scattered light. This process relies on the electric polarizability of the particles.

The intensity of this scattering depends heavily on the wavelength of the light. In the normal dispersion regime, the amount of scattering is inversely proportional to the fourth power of the wavelength. This means shorter wavelengths scatter much more intensely than longer wavelengths. Blue light has a shorter wavelength than red light. Therefore, blue light is scattered far more effectively as it moves through the air.

This is why the diffuse sky radiation we see during the day is blue.

There are different ways to categorize light scattering based on particle size. Rayleigh scattering applies when the particle is very small. Specifically, the particle size must be less than one-tenth of the wavelength. When particles are larger or comparable to the wavelength, we use different models. These include Mie theory and the discrete dipole approximation. For particles that are optically soft but larger, we use anomalous diffraction theory.

The history of this discovery involves several important scientists. In 1869, John Tyndall noticed that light scattering off nanoscopic particles had a blue tint. He suspected this caused the blue sky but could not explain why blue light was preferred. In 1871, Lord Rayleigh published papers to quantify this effect. He studied how particle volume and refractive indices affected the light. By 1881, he used electromagnetism to support his equations. In 1899, he proved the theory applied to individual molecules.

We can see the significance of these physics through specific measurements. Nitrogen is the major constituent of our atmosphere. At a wavelength of 532 nanometers, which is green light, nitrogen has a specific Rayleigh cross-section. At standard atmospheric pressure, there are about $2.5 imes 10^{25}$ molecules per cubic meter. This density means that for every meter of travel, a small fraction of light is scattered. This precise math allows scientists to predict how much light will reach an observer from different angles.

Rayleigh scattering creates many notable visual examples. At twilight, the sun is low on the horizon. The sunlight must travel through much more atmosphere to reach the observer. During this long journey, the blue and violet light wavelengths are scattered out of the direct path. This leaves the yellowish to reddish hues we see at sunset.

You can also see dramatic effects in monochromatic rainbows.

This phenomenon also connects to other fields like material science and engineering. Rayleigh scattering occurs in amorphous solids, such as glass. It is a cause of energy loss in optical fibers made of silica. These fibers have microscopic variations in density and refractive index. It also affects how sound waves move through granular matter. Even porous materials, like sintered alumina, can show Rayleigh-type scattering due to their tiny pore structures.