Shorter wavelengths of light are scattered more than longer wavelengths due to a phenomenon called Rayleigh scattering. This scattering behavior is primarily observed when the size of the scattering particles or objects is much smaller than the wavelength of the incident light.
Rayleigh scattering occurs because different wavelengths of light interact differently with small particles or molecules in the atmosphere or other mediums. When light passes through a medium, such as air or water, tiny particles or molecules in the medium can cause the light to scatter.
The extent of scattering depends on the size of the particles relative to the wavelength of the light. In Rayleigh scattering, the scattering particles are significantly smaller than the wavelength of the light. As a result, the intensity of scattered light depends on the fourth power of the wavelength.
Mathematically, the intensity of Rayleigh scattering is inversely proportional to the fourth power of the wavelength. This means that shorter wavelengths, such as blue and violet light, are scattered much more than longer wavelengths, such as red and orange light.
To understand why shorter wavelengths are scattered more, consider that the smaller particles or molecules interact more efficiently with shorter wavelengths. The electric field of the incident light induces oscillations in the charged particles or molecules, and the scattered light is radiated in various directions. The scattering efficiency increases with decreasing wavelength, leading to more scattering of shorter wavelengths.
This is why the sky appears blue during the day. The shorter wavelengths of blue light are scattered more by the tiny gas molecules in the Earth's atmosphere, causing the blue light to be scattered in all directions. In contrast, longer wavelengths of light, such as red and orange, are less affected by Rayleigh scattering and can travel through the atmosphere relatively unimpeded, which is why sunsets and sunrises often display warm hues.
Overall, Rayleigh scattering explains why shorter wavelengths of light are scattered more than longer wavelengths, leading to the characteristic scattering and color phenomena observed in our atmosphere and other scattering mediums.