Electromagnetic decay inside materials.

[Squires]

Hey guys, back again for some help if that's okay!

I've derived a formula for an electromagnetic wave entering a material, as $\underline{E}$e$^{-\frac{x}{\delta}}$e$^{i(\frac{x}{\delta}- \omega t)}$

x=direction of propagation
t=time
$\delta$=skin depth

As you can see this describes the wave propagating into the x direction, but also decaying.

My question asks to relate this decay inside a metal to the appearance of the metal surface, when the metal is smooth.

My attempt at this solution is that the decay will be greater, as the skin depth is larger.

Then the skin depth increases as the conductivity of the material decreases.

But then I'm stumped. I looked online for things such as, are higher conducting materials shinier than lower conducting materials? Or is this just too vague of an approach would you think? And is it even correct?

 

[Nate810]

Any help would be much appreciated!It's difficult to directly relate the decay of an electromagnetic wave to the appearance of a metal surface. The skin depth is related to the conductivity of the material, but not necessarily the appearance. However, there are some indirect relationships that you can consider. For example, higher conductivity materials may be more reflective, and thus appear shinier than lower conductivity materials. It's also possible that higher conductivity materials may have a smoother surface structure which can increase reflectivity and make them appear shinier.