Wave in air vs. wave in the medium (same frequency)
The medium wave has a shorter wavelength and travels slower: v = c/√(μrεr). Both oscillate at the same frequency.
Reflection & transmission at the air/medium interface
Normal incidence. Γ uses the (possibly complex) intrinsic impedance η = √(μ/ε_c).
Skin depth: field decay into the conductor
δ = 1/√(π f μ σ): the depth where the field falls to 1/e of its surface value.