The complex part nc of the refraction index n determines how far an e.m. wave of wavelength λ can survive crossing a specific medium. The attenuation length la is the distance after that the amplitude of an e.m. signal reduces its value by an amount of 1/e. For instance the amplitude of the Electric field E(z) of an e.m. wave proceeding along the z direction is decreasing as exp(-z/la) being la=λ/(2𝜋 nc) the attenuation length associated to that specific material (nc) and wavelength λ. This way attenuation length in water can be of hundreds of meters in the visible range and just few microns in the microwaves. So that penetration of radiation in the matter depends on both, the specific (dielectric) properties of the matter (through nc) AND the specific wavelength λ of considered e.m. signal.