AcademyLight Propagation
Academy
Scattering
Level 1 - Physics topic page in Light Propagation.
Principle
Scattering redirects light when it interacts with particles, molecules, or irregular structures. The strength and direction of scattering depend on wavelength and the size of the scatterers.
Notation
\(I\)
light intensity
\(\mathrm{W\,m^{-2}}\)
\(\lambda\)
wavelength
\(\mathrm{m}\)
\(a\)
typical scatterer size
\(\mathrm{m}\)
\(\theta\)
scattering angle
\(\mathrm{rad}\)
\(\sigma\)
scattering cross-section
\(\mathrm{m^{2}}\)
Method
Derivation 1: Identify the size scale
If scatterers are much smaller than the wavelength, Rayleigh scattering is a good model. If scatterers are comparable to or larger than the wavelength, scattering becomes less strongly wavelength-selective.
Rayleigh size condition
\[a\ll\lambda\]
Derivation 2: Use wavelength dependence
Rayleigh scattering is much stronger for shorter wavelengths.
Rayleigh scaling
\[I_{\mathrm{scattered}}\propto\frac{1}{\lambda^4}\]
Derivation 3: Interpret sky colors
Air molecules scatter blue light more strongly than red light. During sunset, sunlight travels through more atmosphere, so much of the blue light is scattered out of the direct beam and the remaining direct light appears redder.
Rules
Rayleigh scaling
\[I_{\mathrm{scattered}}\propto\lambda^{-4}\]
Shorter wavelengths scatter more
\[\lambda_{\mathrm{blue}}<\lambda_{\mathrm{red}}\Rightarrow I_{\mathrm{blue}}>I_{\mathrm{red}}\]
Examples
Question
Why is the clear daytime sky blue?
Answer
Air molecules Rayleigh-scatter shorter visible wavelengths more strongly. Blue light is scattered into many viewing directions more than red light, so the sky appears blue.
Checks
- Scattering redirects light; absorption converts light energy into internal energy.
- Rayleigh scattering applies when scatterers are much smaller than the wavelength.
- Larger particles often scatter many visible wavelengths more evenly, producing white glare or clouds.
- Scattered sunlight can be partially polarized.