Rayleigh Scattering

Rayleigh scattering is due to the electric polarizability of the particles. Light waves have oscillating electric fields that interact with the charges within a particle, allowing them to move at the same frequency. Therefore, the particle becomes a small radiating dipole whose radiation we observe as scattered light.

The significance of Rayleigh scattering lies in its effects on the color and intensity of sunlight. Sunlight is composed of various colors, each corresponding to a different wavelength. When sunlight enters the Earth’s atmosphere, it encounters molecules such as nitrogen and oxygen, as well as small particles like dust and water droplets. These molecules and particles are much smaller than the wavelength of light.

During Rayleigh scattering, the shorter wavelengths of light, such as blue and violet, are scattered more by the molecules and particles compared to longer wavelengths, such as red and orange. The reason is that the shorter wavelengths are closer in size to the molecular and particle dimensions.

As a result, sunlight scatters more blue light in all directions than any other color when it passes through the atmosphere. This scattered blue light reaches our eyes from all directions, making the sky appear blue.

It is worth noting that if our atmosphere had different molecules or particles, or if the particles were larger than the wavelengths of visible light, we might observe a different sky color.

Rayleigh scattering formula provides a quantitative explanation for the intensity of light scattered by particles much smaller than the wavelength of the incident light. According to Rayleigh’s law, the intensity of scattered light is inversely proportional to the fourth power of the wavelength. As far as the effect of particle size on Rayleigh scattering is concerned, the scattering efficiency increases with decreasing particle size. Smaller particles have a larger surface area relative to their volume, which enhances their ability to scatter light. It is why atmospheric molecules, typically tiny compared to the wavelength of visible light, effectively scatter sunlight.

The Rayleigh scattering formula can be expressed as:

Each term in the Rayleigh scattering formula contributes to our understanding of how light interacts with particles in the atmosphere:

\( I_o \): The incident light’s intensity represents the initial light entering the atmosphere before scattering occurs. As light travels through the atmosphere, it encounters particles that scatter it in various directions.

\( \frac{1 + \cos²θ}{2} \): This term accounts for the angular distribution of scattered light. It emphasizes forward scattering (small angles) and reduces the contribution of light scattered at larger angles.

\( \left(\frac{λ}{λ₀}\right)^4 \): The fourth-power dependence on the wavelength ratio accounts for the wavelength-selective nature of Rayleigh scattering. Shorter wavelengths (blue and violet) are more effectively scattered than longer wavelengths (red and orange).

\( N \): The number density of particles measures how many scattering particles are present in a given volume of air. Higher particle density leads to more scattering.

\( \sigma \): The scattering cross-section characterizes the efficiency of scattering for individual particles. It takes into account the particle’s size, shape, and composition.

The Rayleigh scattering formula highlights the reasons behind the observed blue color of the sky during daylight hours. Additionally, the formula helps explain the varying color of sunlight during sunrise and sunset, where longer path lengths through the atmosphere result in enhanced scattering of shorter wavelengths and a reddish hue.

While the Rayleigh scattering formula provides a solid foundation for understanding light scattering in clear atmospheres, it has limitations. It assumes ideal conditions, such as a uniform distribution of particles and isotropic scattering. In reality, atmospheric conditions can be more complex, leading to deviations from the formula’s predictions. More sophisticated models, like Mie scattering for larger particles, may be necessary in such cases.