Electromagnetic (EM) waves have invoked a lot of interest among scientists and engineers over centuries. And this interest seems to be on the rise, in view of new applications of EM waves being explored and developed, particularly at newer and higher frequencies.
Propagation characteristics of EM wave depend on its frequency (or wavelength), to a large extent. And when an EM wave interacts with an object/material, it undergoes reflection, refraction, scattering, attenuation, diffraction, and/or absorption. Each of these effects are dependent on the frequency of the EM wave(s) because the size of wavelength (relative to the object/material) assumes great significance.
And due to the huge range of frequencies of EM waves employed in various applications these days, they undergo a variety of different effects. This confuses the scientific community sometimes as it is often unclear as to which effect is more dominant at what frequency.
Thus a single mathematical formula (or a small set of formulae) would/could be of great help if different effects (as listed above) and their relative weights can be known at different frequencies. This may be of great boon to young scientists and engineers as it would simplify things particularly for those who are mathematically minded.
This does not confuse the scientific community. It is mostly well understood, and is described well in physics. There is a limit to how simple the explanations can be. As Einstein may have said: "Everything should be made as simple as possible, but no simpler". Just because it is complicated doesn't mean it can be made simpler or easier to understand.
When things do get reduced to one equation (or 4, as in Maxwell's equations), that equation itself is often very difficult to understand.
Whole books are written about how electromagnetic energy behaves and interacts with matter over a particular frequency ranges, and about how it interacts with different kinds of matter.
It is mainly the characteristics of the matter that means different effects happen and different science is involved, and at what frequencies.
Hi M. Salim Beg
Your question has two aspects: object size to wavelength ratio, and also different phenomena that happen for a specific material (regardless of the object size) when interacting with EM waves. Maxwell equations can well describe the interaction between EM waves and objects even for sub-wavelength objects.
Apart from the object size, different things can happen in different frequencies when EM-waves interact with material. All these phenomena can be summarized in the permittivity of the material which describes its response to an external EM field.
Nevertheless, things are already simplified and approximated to get to the Maxwell equations!
Although widely used, they may not be valid for very small distances, and high intensity fields.
Mohammad Esmail Aryaee Panah
Not all these phenomena can be summarized in the permittivity of the material. For a start there is the permeability, which is as basic as the permittivity, then whole areas that these two do not cover at all, such as fluorescence, ionisation, photo-electricity, Rayleigh and Raman scattering, interaction with (other) fundamental particles, interaction with gravity/space-time, and more.
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