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Sorry if this is an easy question, I am new to physics and this field.

I have a question about reflectance which i believe to be "effectiveness of reflecting radiating energy"

My goal is to make a simulator that graphs the reflectance of a material at different frequencies of wave hitting it. However I am stuck on the equations

I have been looking through the fresnel equations and found no reference to wavelength in any of them. Moreover most examples seem to be for visible light which I'm not interested in (I will mostly be simulating in high GHz bands)

So, my question is:

Is there an equation where I can calculate reflectance for a given frequency and a given object (obviously the object would have different refractive index etc.)

Qmechanic
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Taylor
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    Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. – Community Jul 23 '22 at 07:29
  • For simulation we are relying on measured BRDF. https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function It takes e.g. small structures from milling a metal into account. For idealised polished metal the refractive index+Fresnel is sufficient http://refractiveindex.info/ – Stefan Bischof Jul 23 '22 at 13:17

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Fresnel Equations work for RF/THz frequencies just fine (although they don’t include diffraction, which might also be relevant). The frequency dependence comes in through the material’s electromagnetic impedance, $\eta$. If it’s a non-magnetic material, you can use the refractive index, $n$, instead (which is probably what your reference uses). You need to find $n$ for the material and frequency of interest. Make sure you have the complete complex value!Then you plug it into the Fresnel Equations like usual.

In that frequency range, you might not find $n$ in the literature but instead find dielectric permittivity, $\epsilon$, or conductivity, $\sigma$. But that’s okay; you can convert from one to the other by using $$ n = \sqrt{\epsilon_r}, $$ where $\epsilon_r$ is the relative permittivity, and as described here.

Gilbert
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  • So you're saying plug in electromagnetic impedance instead of reffractive index in the fresnel equations? Basically what im trying to work out is how someone made this first picture on this wikipedia page https://en.wikipedia.org/wiki/Reflectance#Radiometry_units_in_the_International_System_of_Units – Taylor Jul 23 '22 at 15:30
  • @Taylor feel free to use refractive index, as Al, Ag, and Au are all non-magnetic. Plug in their frequency-dependent complex refractive index, and you will produce those curves for the power reflectivity, i.e. the absolute value of electric field reflectivity, squared. – Gilbert Jul 24 '22 at 00:51