Shorter wavelengths of light are scattered more than longer wavelengths due to a phenomenon called Rayleigh scattering. Rayleigh scattering occurs when the size of the scattering particles or structures in a medium is much smaller than the wavelength of the incident light.
When light interacts with particles or structures in its path, it can be absorbed and re-emitted in different directions. The intensity of scattering depends on the size of the scattering particles and the wavelength of the incident light. In Rayleigh scattering, the scattering particles are much smaller than the wavelength of light, and as a result, the scattering intensity is inversely proportional to the fourth power of the wavelength.
Mathematically, the intensity (I) of Rayleigh scattering is proportional to (1/λ)^4, where λ represents the wavelength of light. This relationship means that shorter wavelengths are scattered more strongly compared to longer wavelengths.
To understand why shorter wavelengths are scattered more, consider that the scattering particles act as tiny antennae, re-emitting the incident light in various directions. Since the size of the scattering particles is much smaller than the wavelength of the light, shorter wavelengths interact more with the particles, causing stronger scattering. In contrast, longer wavelengths experience weaker interactions and are scattered to a lesser extent.
This phenomenon is why the sky appears blue. When sunlight passes through the Earth's atmosphere, the shorter blue and violet wavelengths are scattered by the tiny gas molecules in the air, such as nitrogen and oxygen. The scattered blue light is then observed in different directions, giving the sky its blue color. In contrast, the longer wavelengths of light, such as red and orange, are less affected by Rayleigh scattering, allowing them to travel through the atmosphere and reach our eyes, which is why the sun appears yellow or red during sunrise or sunset when the light must travel through a thicker atmospheric layer.
In summary, shorter wavelengths of light are scattered more than longer wavelengths due to Rayleigh scattering, which occurs when the scattering particles or structures in a medium are much smaller than the wavelength of the incident light.