## Ecran trop petit

Le calculateur n'est pas disponible sur téléphones. Largeur de 960px minimum.

### Parameters

• Mie calculation
• Colour calculation
Transmission
Scattering

# Mathematics

The calculation of the cross-section is done using a PiMieScatt library. It uses Mie theory to determine the effeciences and cross-section using the dielectric functions of the metals. There is an automatic determination weither to use rayleigh based on the size of the particle.

## Calculation cross-section

When $$a \ne 0$$, there are two solutions to $$ax^2 + bx + c = 0$$ and they are $x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$

To determine the transmission and scattering intensities, the Beer-lambert equations are adapted as follows: $I_{trans} = I_0 \, e^{\sigma_{ext} \, n \, x}$ $I_{scatt} = \frac{1}{2} \,\beta \,I_0 \,\frac{\sigma_{sca}}{\sigma_{ext}} (1-e^{-2 \, \sigma_{ext} \, n \, x})$