The complex part nc of the refraction index n determines how far an electromagnetic wave of wavelength λ can survive crossing a specific medium. The attenuation length la is the distance after that the amplitude of an electromagnetic signal reduces its value by an amount of 1/e. For instance the amplitude of the Electric field E(z) of an electromagnetic 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. The opposite happens over solid land surfaces where optical waves can penetrate from few microns up to few millimeters (moving from the VIS-NIR to the TIR spectral range) whereas microwaves can reach depths from hundreds to towsands (as higher are their wavelength) meters allowing the exploration of subsoil and thick coulters of ice.
Explain what the attenuation length and penetration depth are
Compare and discuss attenuation length and penetration depth of the optical and radar signal
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