If both radio waves and gamma rays can travel through walls and they are on opposite ends of the electromagnetic spectrum, then why can't light travel through walls which is right in the middle of the spectrum?  
This question has already been asked here. However, I am not entirely satisfied by the answer given on that page which relies on fanciful analogies and metaphors of ants, elephants etc. I am looking for a better explanation.  
I think the crux of the matter, and my dilemma, relates to formula for penetration depth. This is a well known formula used to explain the fact that low frequency waves have more penetration than high frequency waves.   
But then how come gamma waves have such high penetration?   
Are there some assumptions behind derivation of this formula which break when we consider very high frequency waves?  
Or, are there some new factors that need to be taken into account as we move into the high frequency regime?   
If given a radio source and a gamma source of equal intensity, then will the radio source have more penetrability than the gamma source per formula for penetration depth? If not, why not?
Thanks for all those who posted answers to this question. The answer being proposed is that light waves have the right energy to interact with atoms and electrons in the matter and thus get absorbed. This is a quantum mechanical explanation. The skin depth, on the other hand, is derived purely on basis of classical electrodynamics. So I see there are two mechanisms at work here? Does anyone agree with this? If so, the net absorption will be the sum of absorption due to skin effect + absorption due to atomic physics. Now if we take gamma rays - agreed there will be no absorption due to atomic physics but there should be absorption in accordance with skin effect. And so I come back to original problem.
 A: A high-energy electron can go through a wall.  A bulldozer can go through a wall.  
But a small dog cannot go through a wall.
Same difference.  
Further, radio waves can't go through a metal wall, only a wall made of an insulator.  
Gamma rays going through a wall do damage to the wall on the microscopic scale, like the bulldozer.  Light is high enough energy that it "bounces off" even an insulator, (radio waves "bounce off" metal walls).
A: I think this is also a case of "all else being equal" not being equal. At low enough frequency, radio waves will penetrate a practically arbitrary thickness of lead (skin effect), because radio waves have low enough energy (in the sense of Planck's formula) that they can excite electrons in unison and induce currents without being absorbed/scattered (the energy they temporarily transfer to the metal is returned through induction).
On the other hand, 1 cm of lead will stop quite a bit of gamma rays, because gamma rays have enough energy to fill the energy levels in the material, and then some. This can be stated differently by looking at the scattering cross-section of gamma rays interacting with lead atoms.
Now somewhere in the middle of the spectrum lies visible light, and it is informative to ask why visible light will penetrate some materials and not others. Again, the answer is (almost) the same. A material such as lead has unoccupied (electron) energy levels that are just right so that if visible light is incident upon the material, electrons can be promoted to these levels if the light is absorbed. A material such as glass has a large "gap" or absence of energy levels, so electrons must acquire much more energy before they can populate these levels. If they don't acquire enough energy to go into these levels, they simply won't absorb the energy. If they do, they will (which is why glass is largely opaque to UV light).
The only thing that really makes the different parts of the electromagnetic spectrum behave differently is the avaiability of energy levels in most materials. Radio waves and microwaves and far infra-red, and the like do not have enough energy excite atomic energy levels (however they can excite vibrational energy levels). Near IR and visible light can excite atomic energy levels, while UV and X-rays can ionize atoms. X-rays have enough energy to cause structural (kinetic) damage beyond ionization, while gamma rays can split nuclei.
A: Photons interact with matter if the matter offers quantum transitions that match, or nearly match, the photon's energy in the inertial frame of the matter.  Ordinary matter such as wood, stone, etc. offers several groups of possible quantum transitions. 


*

*Rotation of molecules (if they are free to rotate, i.e., not condensed matter)

*Vibration of molecules - bending, quivering actions

*Electronic excitations

*Nuclear excitations (there being various kinds, ignored here for simplicity)


Microwaves have such low energy they can't do much, though they might excite some types of vibrations on larger floppier molecules - however, any type of molecule that could be described as "floppy" probably isn't good for construction materials.  Rotational modes aren't possible in a strong material made of crosslinked polymers or silicates.  So microwaves mostly fly right through.
Near-infrared and visible light can kick electrons into higher molecular orbitals.  Even if the energies aren't a match, just close, there is interaction, as Heisenberg lets them cheat temporarily. Also, having more energy, visible light photons can stir up a greater variety of vibrational modes.  There's nothing in common wall materials to prevent that, and in fact, the interaction with photons is so strong that the material, if not super-thin (microns), will be opaque.  Of course, glass is an exception.
Gamma rays are of such high frequency, electrons (or ions, or polarized ends of molecules) can't keep up due to inertia - so no interaction, or only a little.  At the right frequencies, gamma photons can interact with nuclei, but for a randomly chosen source of gammas, its photons are unlikely to match closely enough with any of the available nuclear excitations, and can't really do much at the molecular level - therefore, the material is almost transparent.
All this is so oversimplified...
A: The anthropocentric explanation is that if visible light rays could go through wood or plaster we would not build walls with wood or plaster.
