Penetration depth

Penetration depth is a measure of how deep light or any electromagnetic radiation can penetrate into a material. It is defined as the depth at which the intensity of the radiation inside the material falls to 1/e (about 37%) of its original value at (or more properly, just beneath) the surface.

When electromagnetic radiation is incident on the surface of a material, it may be (partly) reflected from that surface and there will be a field containing energy transmitted into the material. This electromagnetic field interacts with the atoms and electrons inside the material. Depending on the nature of the material, the electromagnetic field might travel very far into the material, or may die out very quickly. For a given material, penetration depth will generally be a function of wavelength.

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

If ${\displaystyle \delta _{p}}$ denotes the penetration depth, we have

"Penetration depth" is one term that describes the decay of electromagnetic waves inside of a material. The above definition refers to the depth ${\displaystyle \delta _{p}}$ at which the intensity or power of the field decays to 1/e of its surface value. In many contexts one is concentrating on the field quantities themselves: the electric and magnetic fields in the case of electromagnetic waves. Since the power of a wave in a particular medium is proportional to the square of a field quantity, one may speak of a penetration depth at which the magnitude of the electric (or magnetic) field has decayed to 1/e of its surface value, and at which point the power of the wave has thereby decreased to ${\displaystyle 1/e^{2}}$ or about 13% of its surface value:

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