There is a related question (Why glass is transparent?) but I am coming at it only from Maxwell's equations. One can determine the skin depth $δ$ for poor conductors like (pure) water and glass using (see Wikipedia)
$$δ =2ρ \sqrt{\frac{ϵ}{μ_0}}$$
If I ignore the frequency dependence of the permittivity (only to get a board range for the skin depth of glass), using appropriate values for the resistivity ρ (water = $2.5×10^5$ Ω∙m and glass = $10^{10}−10^{14}$ Ω∙m), electric permittivity ($ϵ=ϵ_0ϵ_r$) and magnetic permeability ($μ ≈ μ_0$), I calculate that
$$δ(water) =10^4m$$ $$δ(glass) =10^8-10^{12} m$$
Maxwell’s equations determine the behavior of electromagnetic waves in conductors (as well as poor conductors), so if glass and water have such larger skin depths, then this is the reason why light is transparent for these two mediums – right? If so, I then have two related questions:
Mathematically, it’s fairly straight forward to show that the skin depth is independent of frequency. However, is there a physical explanation why the skin depth is independent of frequency for poor conductors but not for good conductors?
At least at optical frequencies, the skin depth is mainly dependent on the resistivity of the material. Since glass has a higher resistivity (is a poorer conductor) than water, electromagnetic waves penetrate farther through glass. So the key to understanding why glass is more transparent than water is physically understanding why δ ∝ ρ?
I have looked through the books of Griffiths and Jackson for help on this, and found nothing. Thank you in advance for any help on these questions.
Correction and edit due to Johannes’s comment below for question 2