Foam Mie Scaterring

Shine white light through some foam samples and you see light with a different colour thanks to scattering. Because Rayleigh scattering is to do with dilute, individual particles, the scattering is best described via Mie theory.

Credits

A big Thank You to prof. Steven Abbott for designing and developing the app.

Foam Mie Scattering

 
refractive index nsolid
 
X scale maxim nm
 
 
 
 
wavelength
λ nm
 
 
cells size
φ nm

The scattering from features of typical dimension φ at wavelength λ can be approximated by Mie theory. The scattering depends on the refractive index, nsolid of the cell material (in this case foam cells) compared to the air (or other gas) with n = 1.

Although Mie theory is complex, the van den Hulst approximation does an adequate job. We first calculate a value, p, depending on the refractive indices and the ratio of cell size, φ, to wavelenght λ:

`p=4π(n/n_"solid"-1)φ/(2λ)`

Then the scattering, Q, is given by:

`Q=2-(4/p)sin(p)+(4/p^2)(1-cos(p))`

Now we can plot the data at a fixed λ with varying cell size φ, or at a fixed φ with varying λ.

The plots may throw light on how different wavelengths of visible and IR light interact with the foams, for better or worse.