If you were able to determine some characteristic length of your particle size (distribution !?!) from optical experiments using Mie theory, I would not call this a theoretical prediction of particle size!!

In order to use Mie theory you need the complex (effective) dielectric function of the particles and their surrounding. Then you need to cope with calculating absorption and scattering from this. You will then have to find out, whether the optical experiments stand a chance to be sensitive to size in the range you are interested and in the spectral range you can access.

I do not believe that there's a simple answer for you. The dielectric function may be significantly different from the bulk one, there may be surface modifications, molecules attached and then also particle shape matters. On top of this, all these aspects may be present in form of distributions of relevant parameters.

Try tracing people who have done and published the kind of analysis you wish to do and ask them kindly for their help.

My personal prediction is that unless you do not have very, very uniform and well characterized particle ensembles, it will be very hard to retrieve reliable information.

Finally, study the problem yourself. The file at the link below may be a starter for you. It is one of the first links I got in google. Older books include Born, Bohren and Huffman, Stratton as well as Kreibig and Vollmer as authors. (the latter wrote on metal particles, though).

you may also check:

https://code.google.com/p/scatterlib/

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

https://code.google.com/p/scatterlib/downloads/detail?name=bhmie-matlab.zip&can=2&q=

I didn't know these existed until a minute ago...best of luck

https://www.google.de/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CDAQFjAA&url=http%3A%2F%2Fwww.springer.com%2Fcda%2Fcontent%2Fdocument%2Fcda_downloaddocument%2F9783540336969-c1.pdf%3FSGWID%3D0-0-45-304289-p154406997&ei=ZCY4U8ziB6eBywOfnYIY&usg=AFQjCNE3t2nRGhcjbWXl-g-UGAH7zmR_ig&bvm=bv.63808443,d.bGQ