Penetration of electromagnetic waves through metals In electrostatics we learn that electric field outside a metallic conductor cannot have an influence within the conductor because the dielectric constant of metals tends to infinity. By Maxwell's electromagnetic theory we know electromagnetic waves are composed of both magnetic and electric fields and for the propagation of electromagnetic waves both magnetic and electric field should exist. Then how are gamma rays able to penetrate through thin sheets of metal?
By using the formula $c=\frac{1}{\sqrt{\mu \varepsilon}}$ we get that for metals the speed of any electromagnetic wave should be zero. Then how are some electromagnetic waves blocked by metals and some like gamma rays able to penetrate through thin layers of metals?
 A: At high frequencies the skin effect is so strong that the current flows only through a very thin surface layer. As the frequency increases, this layer becomes thinner making its resistance higher. As a result, metals are not good conductors at very high frequencies.
In turn, dielectrics don't have free electrons and cannot conduct low frequencies that require electrons to move between atoms. However, at high frequencies electrons don't move, but only oscillate where they are. Thus very high frequencies do not require electrons to leave their atoms, but only oscillate (in the classical sense) around their atoms. As a result, some dielectrics become conductive at very high frequencies.
For example, the visible light frequency is in hundreds of terahertz. Metals are not conductive at such frequencies, but a glass optical fiber is.
To answer your question, metals are not conductive at gamma-ray frequencies and cannot stop gamma-rays based on the electron conductivity logic. The frequency of gamma-rays is generally too high for electrons to interact with. Gamma-rays are normally emitted and absorbed by the nucleus of an atom.
A: If you are talking about a static external field, you can think of the electrons inside a metal as free-flowing, thus they will align themselves just the right way to counteract the external field, which results in no net field inside the metal. This is the theory behind Faraday's cage, which protects you from lightning.
When it comes to radiation, things get more complicated. According to Maxwell, radiation is composed of alternating E and H field components, and following Maxwells equations, you can derive a diffusion equation for the field strength inside the metal, which decreases exponentially with depth. This is called the skin-effect, and the skin depth is defined as the depth where the initial field intensity is reduced to 1/e (37 %), which is often regarded (for simplicity's sake) as the penetration depth. The general rule says the skin depth decreases with the inverse root of the frequency.
When it comes to optical frequencies, there are lots of different effects (like electronic resonance), which result in absorption peaks. For some metals, the Drude-Lorentz model is a good approximation of optical behavior.
I am unfamiliar with the interaction of metal and gamma rays, but most likely the two general rules still apply.
