# Mie Theory.

1. Feb 23, 2008

### stevenbarea

Hello, can anyone tell me the equation to the Mie scattering.

I have salt particles of a specific size, and I want to work out the Mie scattering of it.

Thanks a lot
From steve.

2. Feb 23, 2008

### Tom Mattson

Staff Emeritus
I had never heard of Mie theory before today, and I do not know the equations. But I Googled it and found the following web-based Mie theory calculator. Of all the dumb luck! :rofl:

http://omlc.ogi.edu/software/mie/

3. Feb 23, 2008

### _Mayday_

I found that aswell Tom, it's amazing how easy it is to find something you know nothing about on google. 5 minutes and you've got it.

4. Feb 25, 2008

### Andy Resnick

Mie scattering is the scattering of a plane wave by a sphere. The equations are too complicated to write down here, but the procedure to obtain them is fairly straightforward, and can be generalized somewhat to more complicated shapes: ellipsoids, cylinders, concentric spheres, etc.

Van de Hulst's "Light Scattering by Small Particles" (Dover) is a good place to start, but the terminology is a little dated. I learned it from a prof. who generated his own book from class notes, it's much easier to follow but not publicly available.

The calculator referenced above is pretty impressive! There's another page with all kinds of available codes, some may be more applicable.

http://www.t-matrix.de/

5. Feb 25, 2008

### stevenbarea

So there is no definite equation for the Mie Theory, that can give me the scattered angle, knowing the intensity and radius of particle under investigation?

If this is the case I would have to use MiePlot which would essentially give me the size of the particle under investigation?

Thanks.

6. Feb 26, 2008

### Andy Resnick

There is no single "scattered angle". There is most certainly a definite closed-form solution, but as I said, it's too much to write down here, especially since there's tons of material out there. MiePlot is a great place to start, if you are wholly unfamiliar with light scattering.

Usually, a detector is placed at 90 degress from the source in a device, for signal-to-noise considerations. But using several detectors, at specific fixed angles, can be used to give better accuracy.

7. Feb 26, 2008

### stevenbarea

Well the thing is, I have the voltage for each scattered angle, by moving a sensor. And I've plotted voltage vs scattered angle using Excel. And then using MiePlot I've tried entering values for size of particle, until I got the MiePlot graph to be more or less the same as the graph of voltage vs scattered angle using Excel. Is this another way of roughly working out the size of the water particle? Do I have to convert voltage values into intensity values first?

Thanks a lot

8. Feb 26, 2008

### Andy Resnick

If voltage is linearly dependent on intensity, then no.

The scattering generally varies as a function of both particle size and refractive index, tho- have you controlled for the refractive index? Dispersion will mess up your (admittedly useful) kludge.

There's also a lot of twiddly effects that come into play if your detector is sensitive enough to pick them up (i.e. tightly selecting for scattering angle): look up morphological-dependent resonances (MDR), for example.

9. Feb 26, 2008

### stevenbarea

Yea I did control the refractive index, I set it to air. I manage to set everything according to the factors in my experiment. I'm just curious though the MiePlot graph is sort of an exponential decay one, with two smaller peaks as it exponentially decays. And the graph i produced using excel which is the intensity vs scattered angle graph, looks the same, what effect is this? why are there smaller peaks?

10. Feb 28, 2008

### Andy Resnick

In light scattering, what matters is the *relative* refractive index: did you also control for the refractive index of the particles?

The generic scattering pattern obtained will have side-lobes, IIRC those are the primary (and supernumerary) rainbows. In the ray-optics picture, the lobes appear from constructive interference between rays with different paths through the particle, which is also the origin of MDRs.

The reason most light scattering plots are done logarithmically is to emphasize these low-amplitude scattering lobes, which is where information about the scatterer lies.

11. Feb 28, 2008

### stevenbarea

Oh right so the reason why these peaks appear is due to constructive interference from the diffracted laser beam. What is MDRs, I've been trying to search for it, on the internet but I cant find any relevant resources.

And do IIRC and supernumerary rainbows occur in this experiment or is that just an example of what could happen?

Thanks a lot

12. Feb 29, 2008

### Andy Resnick

I can't tell you about any specific features of your experiment without the data, but yes: rainbows and other effects (glory, Fock transition, Alexander's dark band, etc) are essentially interference effects.

A good web site for atmospheric optics, where a lot of the effects can be seen:

http://www.atoptics.co.uk/

Morphological dependent resonances: Hmmm.. not too much out there. Some papers... nothing general.