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Microwaves, for example, can be reflected off metallic surfaces. This seems counter-intuitive, since the metal's electrons could interact with the electric field component of the EM wave and absorb it.
In fact, you can use a metal grid to polarise microwaves, and there the metal absorbs the microwaves.
So what determines whether an EM wave is absorbed or reflected and how does the reflection happen exactly (I'm assuming in terms of quantum mechanics)
This seems counter-intuitive, since the metal's electrons could interact with the electric field component of the EM wave and absorb it.
In quantum mechanics light is emergent from zillions of photons, and photons as quantum mechanical particles have interactions with the spill field of the lattice that composes metals and (all other solids). It so happens that in metals the optical and lower wavelengths have a high probability of being elastically scattered and thus reflected, that is why metal surfaces make good mirrors. Keeping to classical electrodynamics, this is recorded in the reflectivity of metals.
In fact, you can use a metal grid to polarise microwaves, and there the metal absorbs the microwaves.
"The metal absorbs the microwaves", not in a simple but a more complicated manner Classical elecrodynamics gives a simpler explanation for how the grid functions:
Provided that the wavelength of unpolarized microwave radiation is much larger than the metal grid spacing then the microwave radiation passing through the metal grid is linearly polarized in the direction which is perpendicular to the metal grid and zero radiation is emitted with an electric field component that is parallel to the metal grid. The explanation of this observation involves a consideration of the interaction of EM radiation with the metal wires. Within the metal wires, the mobile free electrons can oscillate at the frequency of the incident microwave radiation. These oscillating electrons acts a dipole source and emit radiation in all directions except in the direction of the oscillation. The transmitted wave is thus a superposition of the incident radiation and the radiation emitted by the oscillating electrons in the wires. However, in turns out that the two sources of radiation are 180o out of phase and cancel each other for the component of the incident radiation which is parallel to the metal wires. So, if the metal grid is in a vertical position and the incident microwave radiation is vertically polarized, zero or very little radiation is propagated in the forward direction.
As the two ways of studying electromagnetism are consistent to each other, the classical framework is easier to understand than the quantum mechanical. It would involve interference effects of photons in a convoluted manner that the classical avoids. See this to understand about how interference effects appear with single photons at a time. In general classical electrodynamics is much simpler because it mathematically describes the behavior of photons with matter in a simpler way.
For metals, whether an electromagnetic (EM) wave is reflected or absorbed is determined primarily by (1) the frequency (or wavelength) of the incident wave, and (2) the density of electrons in the material. This is a consequence of both (a) the response of free electrons to the electric field of EM radiation, and (b) Coulombic forces between these electrons and ionic cores in the metal.
Freely conducting electrons in metals can be collectively be treated as an electron gas whose behavior can actually be described mostly using classical mechanics. In this treatment (see the Lorentz-Oscillator model, a specific example of a driven damped harmonic oscillator), an electron can be accelerated due to a driving force—in this case, the electric field that comprises EM radiation. Other forces affect the electron's motion as well, namely: (1) the Coulombic attraction between electrons and ionic cores within the metal, which provide a restoring force; and (2) damping forces, such as the scattering of electrons off of ion cores.
The combination of all these forces results in a resonant frequency existing for the system. At frequencies below the resonant frequency, input energy is not easily absorbed into the system. (This situation is not unlike a mass on a spring responding to some input force.) Since the energy has to go somewhere, it is instead reflected back outwards. However, at or above the resonant frequency, input energy can be absorbed. For an electron gas in metals, this resonant frequency is called the plasma frequency.
For most metals, the plasma frequency is somewhere in the ultraviolet range, which is far higher in frequency (and thus in energy) than microwaves. This is why microwaves are reflected by sheet metals (the case of mesh grids is different, as they rely on mechanisms that a Faraday cage operates on).
Addendum: there actually is also a quantum-mechanical mechanism for absorption of EM radiation, which is interband absorption—this results from the electronic band structure in all ordered (non-amorphous) materials. Interband absorption explains why some metals are visibly different in appearance (e.g., copper and gold) when these interband transitions occur in the visible region of the EM spectrum. Still, optical properties in most metals are dominated by the position of the plasma frequency rather than interband transitions—hency why most metals have a similar shiny gray/silver reflective appearance.
You are right that there are ample electronic transitions in a metal that match the frequency of optical and lower frequencies. However these transitions do not satisfy momentum conservation. When you apply a grid then momentum is only conserved up to an inverse lattice vector (of the grating). For a suitably choice of grid pitch and duty cycle it is then possible to meet the requirement for a chosen wavelength. Under these conditions light is absorbed.
