# Calculating Mie Scattering of Salt Particles

• stevenbarea
In summary: Thanks for trying!In summary, 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. There is no single "scattered angle". MiePlot is a great place to start, if you are wholly unfamiliar with light scattering.
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.

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!

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

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

stevenbarea said:
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.

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/

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.

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.

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

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.

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?

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.

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 can't 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

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 website 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.

## 1. What is Mie scattering?

Mie scattering is a type of scattering phenomenon that occurs when a beam of light interacts with particles that are larger than the wavelength of the light. It is named after German physicist Gustav Mie, who first described it in 1908.

## 2. How is Mie scattering different from Rayleigh scattering?

Mie scattering differs from Rayleigh scattering in that it takes into account the size of the scattering particles, whereas Rayleigh scattering only considers the particle's refractive index. Mie scattering is typically observed when the particle size is larger than the wavelength of light, while Rayleigh scattering occurs when the particle size is smaller.

## 3. What are the factors that affect Mie scattering of salt particles?

The factors that affect Mie scattering of salt particles include the size and shape of the particles, the refractive index of the particles, and the wavelength of the incident light. The concentration and distribution of the particles in the medium can also have an impact on the scattering behavior.

## 4. How is Mie scattering of salt particles calculated?

The calculation of Mie scattering of salt particles involves using Mie theory, which is a mathematical model that describes the scattering of light by particles. This theory takes into account the size, shape, and refractive index of the particles, as well as the wavelength of the incident light. There are also various computer programs and numerical methods that can be used to calculate Mie scattering.

## 5. What are the applications of calculating Mie scattering of salt particles?

Calculating Mie scattering of salt particles has various applications in atmospheric science, remote sensing, and environmental monitoring. It can also be used in the study of aerosols, which are important in air quality and climate research. Additionally, Mie scattering is used in industries such as pharmaceuticals, cosmetics, and food processing to determine the size and concentration of particles in products.

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