How to understand the refractive index of metals

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The refractive index of polycrystalline silver at 633 nm is characterized by n=0.135 and k=3.999, indicating that it has both a real and imaginary component due to absorption. The term "nk" refers to the complex refractive index, where 'n' represents the phase velocity of light in the material and 'k' indicates the extent of absorption. The wavelength in silver is not calculated as 633/0.135 nm; instead, the refractive index describes how light behaves as it enters the metal. Understanding the skin depth is crucial, as it defines the limit to which light can penetrate the material. For a deeper understanding, refer to the relevant chapters in Born & Wolf's "Principles of Optics."
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for an example, polycrystalline silver, its index is n=0.135 and k =3.999 at the wavelength of 633nm, what does the nk mean, is that telling us the wavelength in the silver equals 633/0.135 nm ? and how to calculate the refractive angle in the metal?
Give a good explanation, please.
 
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Silver is a metal, which has a skin depth, after which the incident radiation does not penetrate any further. Look in the later chapters of Born & Wolf, Principles of Optics in the chapter about optics of metals. The refractive index is a complex quantity in metals because of absorption.
 
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