This should be a simple question. Given the real part of the refractive index n′ for Silver, approximately 0.05, and applying the relationship for the wavelength inside a material, λ=λ0/n', where λ0 is the vacuum wavelength of green light (around 530 nm), results in a calculated wavelength significantly greater than 10 micrometers. This outcome appears unusually large; is this calculation correct?
Dear Edgar J. Patiño ,
my view onto this topic:
there is another peculiarity related to your wavelength issue;
in addition to the real part n of the complex refractive index nc we have the imaginary part k (nc = n + ik) being k ~ 3,9 in the Ag case*).
The extinction k is related to the attenuation coefficient µ, which describes the exponential decay of the light intensity I passing the distance x (I = I0*exp(-µ*x)) via: µ = 4*pi*k/λ0**)
The 1/e-decay of the intensity is found at a distance of d1/e = 1/µ = λ0/(4pi*k).
For k ~3,9 we will have d1/e ~ λ0/50...
That means that the optical wave collapses within a propagation distance of a very tiny fraction of its own primary wavelength in the Ag. Thus no wave propagation will occur in the Ag and a question about a wavelength is, to my opinion, meaningless here.
The pictorial imagination of the model of wave propagation fails here under these strong parameters n and k. But fortunately the mathematics still works and the outcomes fit to the experimental results such as for example the reflectivities...
*) https://refractiveindex.info/?shelf=main&book=Ag&page=Johnson
**) https://en.wikipedia.org/wiki/Refractive_index#Complex_refractive_index
or any optics book
Best regards
G.M.
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