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This is the generic form of a dispersion relation with a low frequency cutoff. It is a good model for the dispersion relation of electromagnetic waves in a plasma, i.e. the ionosphere, where: $$ \omega^2 = \omega_0^2 + c^2 k^2 $$ Which is the same as your form, though I've put back in $c$ for the nondispersive phase velocity and changed $k_0 \to \omega_0$ ...


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I start my answer with the the second question (similar situations). This is eerily similar to the free-particle dispersion relation (or the relativistic energy-momentum relation) in natural units ($c = 1$ and $\hbar = 1$), $$\omega^2 = k^2 + m_0^2$$ This system of units is commonly adopted in particle physics and quantum field theory. It can be clearly ...


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I'm not sure what goes into a film emulsion. As to small particles, it's basically the black-body principle. No material is perfectly reflective, so the more reflections a light ray undergoes, the more attenuation occurs. A pile of tiny particles essentially acts as a "light trap." One of the better absorbing materials (up until the development of ...



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