Penetration depth

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When light or any electromagnetic radiation is incident on the surface of a material, part of it is reflected and part transmitted into the material. This EM Wave interacts with the atoms and electrons inside the material. Depending on the nature of the material, the EM Wave might travel very far into the material, or on the other hand die out very quickly.

Penetration Depth is a characteristic of the material and is a measure of how deep can an EM Wave penetrate into the material. For a given material, penetration depth can vary for different wavelength of EM Wave, and usually, is not a fixed constant.

According to Beer-Lambert law, the intensity of an EM wave inside a material falls off exponentially from the surface as

$I (z) = I 0 e - α z$

The penetration depth, is quantitatively defined as the depth at which the intensity of the radiation inside the material falls to 1/e of the original value at the surface. Thus if $δ$ denotes the penetration depth, we have,

$\delta = \frac{1}{\alpha}$