Why Do Lightwaves Penetrate Salt Water While Radiowaves Cannot?

[Thierry12]

Can someone explain to me the equation on complex conductivity found here :
http://farside.ph.utexas.edu/teaching/jk1/lectures/node58.html"

I am trying to understand why lightwaves penetrates salt water (conductor) but radiowaves can't.

 

[Xezlec]

Good observation. The fact that light waves have a skin depth much deeper than what that formula seems to say they should is interesting, isn't it? But let's look at our assumptions. What numbers did you plug into the formula? The frequency of light is easy to find out. The magnetic permeability is a constant. But where did you get your value of conductivity of salt water? Is conductivity of salt water a constant?

I would think the answer to this question lies in the fact that salt water conducts by big, heavy ions (from the salt) moving around. And big, heavy ions don't like to move around as fast as TRILLIONS of Hertz (the frequency of light). This means that the resistance to extremely high frequencies would be extremely high. So the conductivity at a hundred trillion Hertz isn't the same number as the conductivity at DC (0 Hz), which is probably what you looked up.

The moral is: don't assume a number like conductivity of a substance is a constant! It may depend on other circumstances, like frequency.