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Why can visible light, which lies in the middle between X-ray and radio waves in terms of frequency/energy, not penetrate walls?

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The interaction of photons with matter is complicated. The electromagnetic spectrum covers many orders of magnitude in frequency and photon energy, and there are qualitatively different processes that occur in different regimes. The results depend on the electrical properties of the material, such as conductivity and permittivity. We have materials like glass that are transparent to visible light, and low-energy x-rays that are strongly absorbed.

But speaking very broadly, it is possible to understand the main trends over the whole spectrum. We have a region (1) in the visible spectrum, where the frequency of the light is similar to the frequency of condensed-matter resonances, which in many cases you can think of as resonances of the electrons, as if the electrons are little objects attached to atoms by springs; and region (2) in low-energy x-rays, where the wavelength of the photon is comparable to the wavelength of the electrons in an atom. This splits up the spectrum into three parts.

At low frequencies $f$, below region 1, we have a skin depth, which depends on $f^{-1/2}$. As $f$ gets smaller, the skin depth grows without bound. Hence radio waves tend to be penetrating.

Around region 1, you get strong classical resonant behavior. You can see this if you look at a plot of the index of refraction of glass as a function of frequency. It has a series of spectacular peaks. Each of these peaks has a classic Lorentzian shape, in which the response on the right-hand side of the peak approaches zero. So if you ignore the peaks themselves, which are narrow, then you get a series of stair steps. At frequencies above region 1, you've gone down all the stair steps, and the response approaches zero. This is why, classically, we expect high-frequency electromagnetic radiation to interact with matter very weakly.

But in region 2 you get the photoelectric effect. In first-order perturbation theory, this depends on the extent to which the electric field overlaps with the wavefunction of the electron. When the two wavelengths are similar, you get a strong cross-section. This is why matter strongly absorbs soft x-rays, but not gammas and hard x-rays.

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  • $\begingroup$ Interesting, I met something similar in optical fiber transmission frequencies windows at IR around values:(850, 1300 and 1550 nm) $\endgroup$ – Amr Berag May 31 at 18:42
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To understand what radio waves are, please read about What are photons, electromagnetic radiation and what are radio waves.

The thickness of a wall

You should have no problems with X-rays.
The moment of such photons is simply strong enough to penetrate materials. Without interacting with the wall, they exit the wall with the same wavelength (I prefer to talk about the same energy, frequency and moment).
Or they exit with a reduced energy due to absorption and re-emission with the subatomic particles. We observe the energy difference between the incoming and outgoing photons as an increase in temperature of the material.

With the right material (lead) or with the right thickness for any material you are able to capture X-rays inside the material. On the other hand, you are able to transmit visible light even through metal. It's all about thickness. Gold or aluminum can be made so thin that light can pass through it.

Reflection from surrounding obstacles vs. closed rooms

Take a spotlight with a wide lighting angle and point it at the wall. The surrounding reflective obstacles will cause the wall to be illuminated from the other side. A distant radio source is like a very large transmitter (spotlight). The surrounding obstacles also reflect the radio waves.

On the other hand, it is possible to build a closed room in which neither visible light nor radio waves can illuminate a wall inside the room.

In these cases everything revolves around the experimental setup.

The real difference

Radio waves have two properties that light from a thermal source does not have.

The photons of a radio wave are polarized. Every half period of the wave generator the influenced skin electrons change their direction of acceleration and emit photons with the electric field component up or down (in case of a vertical antenna rod). The radio wave is a polarized radiation.

Furthermore the radio wave is by its nature (technical concept) a radiation with periodic intensity.

These two properties could influence the material of a wall. Phonons are one way in which radio waves penetrate a wall with their "synchronized" photons. By analogy, take a hanging metal sheet and blow on it with a certain intensity. The sheet is lifted a little bit. If you do the same with the same energy content, but periodically with a higher intensity, the sheet can be resonated and periodically lifted so that more air gets behind the hanging sheet.

Periodicity and polarization - I am sure that these two properties of radar on surfaces should be suppressed in order to be successful in stealth technology.


Edit

Quote from Wikipedia about molecular oscillations from radio waves to heat:

One of the most commonly known types of RAM is iron ball paint. It contains tiny spheres coated with carbonyl iron or ferrite. Radar waves induce molecular oscillations from the alternating magnetic field in this paint, which leads to conversion of the radar energy into heat. The heat is then transferred to the aircraft and dissipated.

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  • $\begingroup$ Nice answer. "Gold or aluminum can be made so thin that light can pass through it." can you elaborate on this please? $\endgroup$ – Árpád Szendrei May 30 at 16:03
  • $\begingroup$ @ÁrpádSzendrei Goldbeating. And through an aluminum foil like you have it at home to wrap something, a laser is shining. The same for a the blade of a blade (from steel) $\endgroup$ – HolgerFiedler May 30 at 16:30
  • $\begingroup$ @ÁrpádSzendrei And this answer my you be interested too? physics.stackexchange.com/questions/554586/… $\endgroup$ – HolgerFiedler May 30 at 16:33
  • $\begingroup$ Thickness of barriers is not a valid argument in this context since its a comparison question that can be paraphrased as why can radio waves penetrate some walls that ligh cant? the question is not about extreme advanced sattelites and space telescopes golden planket. In fact I opened this thread protesting closing this one $\endgroup$ – Amr Berag May 31 at 16:53
  • $\begingroup$ It was closed by someone with administration privileges andcfriends felt offended by a humorous comment that I deleted and apologized for but still closing my question because its allegedly about biology. Next I have to come up with a wall material composition that is similar to the human body. $\endgroup$ – Amr Berag May 31 at 16:54
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X rays penetrate matter because their energy is much higher that of any matter excitations. The electrons in matter are to slow and too heavy to react and compensate the field, as they do for optical frequencies. Fort radio wave the opposite applies. They reflect off matter, especially off metals, unless you apply very special coatings. By reflection and diffraction they can go around obstacles and pass through openings.

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