Calculator Inputs
Formula Used
This page uses the small-sphere Rayleigh scattering approximation. It is useful when particle size is much smaller than wavelength.
The calculator is excellent for trend analysis, teaching, and quick engineering estimates. Real molecular scattering can require additional corrections such as depolarization effects and wavelength-dependent refractive behavior.
How to Use This Calculator
- Enter the light wavelength in nanometers.
- Enter the particle radius. Smaller particles fit Rayleigh theory better.
- Provide refractive indices for the particle and the surrounding medium.
- Enter number density to estimate bulk scattering strength.
- Set the scattering angle to see directional intensity changes.
- Choose a reference wavelength for relative λ-4 comparison.
- Press calculate to view results, graph trends, and export CSV or PDF.
Example Data Table
| Color Region | Wavelength (nm) | Relative Scattering vs 550 nm | Quick Interpretation |
|---|---|---|---|
| Blue | 450 | 2.232 | Blue wavelengths scatter much more strongly than green. |
| Green | 550 | 1.000 | This is the chosen comparison baseline. |
| Red | 650 | 0.512 | Red wavelengths scatter far less than green. |
| Deep Red | 700 | 0.382 | Longer wavelengths continue losing scattering strength. |
Frequently Asked Questions
1. What is Rayleigh scattering?
Rayleigh scattering is light scattering by particles much smaller than the light wavelength. Its strength rises sharply as wavelength decreases, which makes short wavelengths scatter far more strongly than long wavelengths.
2. Why does the sky appear blue?
Sunlight contains many wavelengths. Air molecules scatter shorter blue wavelengths more effectively than longer red wavelengths, so the sky looks blue from most viewing directions during daytime.
3. Why are sunsets often red or orange?
At sunset, sunlight travels through a longer atmospheric path. Much of the blue light gets scattered away before reaching your eyes, leaving stronger red and orange tones.
4. When does this model become less accurate?
Accuracy drops when particles are no longer very small compared with wavelength. If the size parameter approaches or exceeds 1, Mie scattering usually becomes a better model.
5. What does refractive contrast mean here?
Refractive contrast compares the particle refractive index with the surrounding medium. Larger contrast usually increases scattering because the electromagnetic field changes more strongly across the particle boundary.
6. What does the scattering angle affect?
The angle changes directional intensity. In this simplified model, the angular factor follows (1 + cos²θ)/2, so forward and backward directions are stronger than 90° scattering.
7. Why is number density included?
Number density converts single-particle scattering into a bulk estimate. Multiplying number density by scattering cross section gives a volume scattering coefficient in inverse meters.
8. Does this calculator model the real atmosphere exactly?
No. It gives a strong educational and engineering approximation. Real atmospheric scattering can include molecular anisotropy, depolarization, wavelength-dependent refractive behavior, and mixed particle populations.