So the general equation for the reflectivity at the interface between two materials is given by: R=(n1−n2n1+n2)2
in case of air/glass n is real, but for, say, semiconductors or metals, where radiation is absorbed, n is a complex number, with n_=nr−ik. k is described as the extinction coefficient and is related to the absorption coefficient with α=4πkλ, λ being the wavelength.
I am looking to derive a formula for the reflectivity which only includes the real and imaginary parts of the complex refractive index. As far as I can tell, the equation above gives the reflectivity as long as the norm of the index is known, that is n1=√n2r1+k21n2=√n2r2+k22
in the above formula for the reflectivity, I replaced the norms of the complex numbers and not the numbers themselves,obviously. So doing that, I get a fraction where square root terms appear. On the other hand Wikipedia writes(https://en.wikipedia.org/wiki/Refractive_index) R=|n1−n2n1+n2|2
which also makes sense and leads to R=(nr1−nr2)2+(k1−k2)2(nr1+nr2)2+(k1+k2)2
Which formula is right?
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