Dear all, during the reading of Absorption and Scattering of Light by Small Particles,i find it difficult to understand the process of Mie theory's calculation for particles' optical efficiency. The question is the book refer to a simplification called far filed approximation based on an imaginary spherical particle. By using this approximation, what can we get? Or it is used for what?
I guess the book speaks about 'far field approximation'. The key example of a far field approximation is if you replace the electromagnetic field of a localized charge distribution by its multipole expansion up to some finite order. More generally, the far field approximation is to a field what an asymptode is to a particle trajectory.
Take a look at:
February 25th, 2014
The life of Gustav Mie and the development of the Lorenz-Mie solution to Maxwell’s equations
https://www.brainshark.com/malvern/vu?pi=zIpzZlnQjz5uTlz0
far fiield means that the distance (at the observer) is large compared to the size of the particle relative to the wavelength of the probe light in formula
distance r >> a2 /lambda; a = particle radius. See for instance
http://www.iapmw.unibe.ch/teaching/vorlesungen/radiative_transfer/skript/Lecture2009_9.pdf
In the far field (as Harry has correctly explained) we have Babinet's principle or assumption (or paradox) that the energy removed from the incident light beam by a particle is twice the particle's cross section (multiplied by the incident flux energy) - one unit removed by the shadowing of the particle and one by the diffraction of energy making 2 units in total. This is where geometric optics (and for particles, the Fraunhofer approximation) applies. Mie theory will show a (correct) maximum in the scattering coefficient dependent on the size and the relative refractive index..This scattering coefficient can be as high as 5 for TiO2 of 300 nm or so meaning that 1 unit of light energy is lost by the shadowing and 4 units by scattering/diffraction. This makes TiO2 the most effective (hiding power) white pigment for paints. See, for example:
August 11th 2011 Optical properties of the three forms of titanium dioxide
http://tinyurl.com/pbgf9hj
and:
October 9th, 2012 The importance of particle size, shape, and rheology in the paints, coatings, and pigments industries
https://www.brainshark.com/malvern/vu?pi=325380838&text=M021507
Alan
Unfortunately I lost my copy of the van de Hulst book on light-scattering in which he describes the phenomenon you mention with the example of a large object in the atmosphere blocking the sun rays when I remember well
Hi Harry It's been available for many years as a Dover reprint. I buy virtually all of my (many!) used textbooks from Abebooks. Here's a world listing (using the wonderful tinyurl.com) of van der Hulsts's classic tome: http://tinyurl.com/glbqffj
You can buy yourself a copy for less than $10 post paid to the Netherlands......
@Harry On Babinet's conjecture and similar things, I wrote this a little while ago based on a conversation with Philip Laven of MiePlot fame - it may be interesting to you and other readers.
Alan
Thank you kindly for your reactions
As for the book: I am retired and work on a manuscripts that deals with visibility reduction during NY fireworks and thus light-scattering,at a practical level (dry integrating nephelometer versus in-situ visibility).
BTW liked your references
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