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My current understanding is that materials found in nature attenuate light as a function of some fixed constant, according to this equation: $ I(x) = I_0 e^{-\kappa_v \rho x} $, where $ I_0 $ is the initial intensity, x is distance inside the material, $ \kappa_v $ is 'opacity', and $ \rho$ is mass density. I am assuming that most materials that I interact with on a day to day basis have some value of $ \kappa_v $ that is between $0$ and infinity. This means if I put an instrument that measured light in a hollow iron sphere which had a wall thickness of say a meter, and put the sphere in orbit around the sun, that a sensitive enough light detector would still be able to pick up some light penetrating the sphere.

Is this correct, or is that equation just some hand-wavey engineering approximation? Are there any materials for which $\kappa_v$ is zero or infinite? I.e. where absolutely no em radiation penetrates whatsoever (maybe a superconductor?) or passes light with zero attenuation of intensity?

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Light passes through a perfect vacuum without attenuation. This is also true for any region in which there are no charged objects to exchange energy with, which rules out anything made of atoms. Maybe pure neutronium?

The answer to Should a superconductor act as a perfect mirror? explains that a superconductor reflects 100% of incident light below a certain frequency. Conservation of energy implies that none of the light can be transmitted. So if you had a low-frequency light source inside a superconducting sphere, you shouldn't be able to detect anything from the outside.

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  • $\begingroup$ It should be noted that pure neutronium does have an admixture of protons and electrons in chemical equilibrium. A perhaps better example is weakly interacting dark matter, which is believed not to interact with electromagnetism at all. Whether it counts as "a material" may be a matter of definition. $\endgroup$ – Anders Sandberg Jul 1 at 7:59

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