Model light scattering from particles with practical precision. Test wavelength, angle, size, and concentration inputs. Generate tables, exports, and graphs for faster optical evaluation.
| Case | Wavelength (nm) | Radius (nm) | Particle RI | Medium RI | Angle (°) | Concentration (#/m³) |
|---|---|---|---|---|---|---|
| Blue laser in water | 450 | 40 | 1.50 | 1.33 | 90 | 1.5e14 |
| Green light latex sphere | 532 | 50 | 1.59 | 1.33 | 60 | 2.0e14 |
| Red light aerosol particle | 650 | 80 | 1.45 | 1.00 | 120 | 8.0e13 |
This calculator applies Rayleigh scattering equations for spherical particles that are much smaller than the incident wavelength in the surrounding medium.
Wave number: k = 2πnm/λ0
Relative index: m = np/nm
Size parameter: x = 2πnma/λ0
Contrast term: ((m² − 1)/(m² + 2))
Differential cross section: dσ/dΩ = k⁴a⁶[(m² − 1)/(m² + 2)]² × angular factor
Total scattering cross section: σs = (8π/3)k⁴a⁶[(m² − 1)/(m² + 2)]²
Scattering coefficient: μs = Nσs
Optical depth: τ = μsL
Transmittance: T = e−τ
Collected detector power: P = I0 × particle count × (dσ/dΩ) × detector solid angle
The unpolarized angular factor is (1 + cos²θ)/2. Parallel polarization uses cos²θ. Perpendicular polarization uses 1. Transitional and large particle regimes should be checked with a full Mie scattering model for higher fidelity.
Light scattering explains how electromagnetic waves change direction after interacting with particles, droplets, defects, or microscopic fluctuations inside a medium. In physics and optical engineering, scattering analysis helps estimate turbidity, particle concentration, haze, beam loss, and detector response. The effect depends strongly on wavelength, particle size, refractive index contrast, concentration, and observation angle.
Very small particles usually follow Rayleigh behavior. In that limit, scattering strength rises sharply as wavelength becomes shorter, which is why blue wavelengths scatter more strongly than red wavelengths in many simple systems. When particles become comparable to wavelength, the angular pattern changes and forward scattering can become much stronger. That transitional region is better described by Mie theory, but Rayleigh equations still provide useful first-pass estimates and scaling trends.
This calculator focuses on the physics quantities most people need during early analysis. It estimates the differential scattering cross section, total scattering cross section, scattering coefficient, optical depth, transmittance, attenuation fraction, mean free path, detector irradiance, and collected power. It also labels the likely scattering regime by using the size parameter. That makes it easier to decide whether the result is comfortably inside the Rayleigh limit or whether a more advanced model should be used.
The graph is especially useful because angular scattering rarely feels intuitive from equations alone. A plotted curve reveals whether intensity remains broad, symmetric, or strongly angle sensitive under the chosen polarization. This is valuable for designing optical sensors, selecting viewing geometry, checking sample dilution, and comparing how radius or refractive index changes affect observed signal. For classroom work, lab preparation, aerosol studies, colloids, and quick optics screening, the calculator gives a practical physics-based starting point.
It estimates Rayleigh-based light scattering behavior for small spherical particles. Outputs include cross sections, attenuation, transmittance, detector response, and the angle-dependent scattering curve.
It works best when the particle size is much smaller than the wavelength in the medium. The size parameter should stay well below one, and preferably below about 0.3.
Shorter wavelengths increase the wave number and strongly raise the scattering terms. That makes blue or green light scatter more strongly than longer red wavelengths in comparable conditions.
It is a dimensionless ratio linking particle radius and wavelength inside the medium. It helps identify whether Rayleigh assumptions remain valid or a Mie model is needed.
Optical depth measures cumulative scattering loss across the chosen path length. Larger values indicate stronger attenuation and lower direct transmittance through the sample.
Polarization changes the angular dependence of scattered light. Parallel, perpendicular, and unpolarized cases do not distribute intensity identically, especially away from forward and backward directions.
They are useful engineering estimates. Real systems also depend on detector area, collection optics, calibration, multiple scattering, and background noise.
Use these results for trend checking, then confirm with a full Mie scattering solver or measured data. Transitional and large particle cases have richer angular behavior.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.