If you have data of absorption coefficient of Al or other metals at each absorption coefficient depending on wavelength, you can calculate that following equation, depth = 1/ absorption coefficient. if you don't have any data for that, you have to obtain it from measurement using by such as ellipsometry or you have to find it from references.
You can also calulate the pentration deph in the ranges of total reflection. Compare to publications dealing with attentuated total relectance and the keyword Fresnel law.
I would suggest, as Michael Schmitt more or less implicated, to use Fresnel equations and tabulated data for the index of refraction. The Fresnel equation and its derivation can be found on wikipedia (https://en.wikipedia.org/wiki/Fresnel_equations). It is important that depending on the incident angle, both the real and the imaginary part contribute to the penentration depth. Optical data down to 30 eV may be found on the centre of X-ray optics webpage (www.cxro.lbl.gov or http://henke.lbl.gov/optical_constants/getdb2.html), but this is clearly not the visible spectral range. Those data might however be obtained from http://refractiveindex.info/, a site that I can also strongly recomment. The reference source of the tabulated data is always given there!
I would only add that there are two factors determining - the frequency and temperature. There are areas of these parameters, which is usually illegal use of the formula d = alpha-1 , alpha=4*pi*kappa/lambda, kappa - ext. coef., that is, we observe anomalous skin layer. Also, we must remember the value d determines the depth at which the power decreases by a factor e=2.72....
Also you can measure the Aspiration coefficient firstly by electrical measurements then you can calculate the depth = 1/ absorption coefficient as mention above by Dr. Nam.
It depends on the material it self ,and also on the optical properties as a function of wavelength whereas the material is transparent to that wavelength or not and as you know R+A+T=1. where R is reflectance , A absorptance. T transmittance.
You, Dr. Pilgun, want to show us a textbook. If you do not understand what the temperature, it is your problem. A comprehensive index of metal ... For there is no refractive index, that's all.
Absorption depth is a useful parameter which gives the distance into material at which lights drops to 36% of its original intensity or alternately has dropped by a factor of (1/e).
It can be calculated based on Beer Lambert laws and by using the relation:
Dear Myroslav I. Kozak, thank you for your directions on the calculation process of the linear absorption coefficient. But could you please elaborate on the second equation which is alpha=4*pi*kappa/lambda and what are those parameters? Actually I am also looking for the values of linear absorption coefficients for H13 tool steel and Ti6AL4V alloy. This discussion helped me to be clear about the difference between the linear absorption coefficient and the absorptance. Thank you all.
Dear Myroslav I. Kozak , I got the meaning of kappa in above equation which is the extinction coefficient. The following link would be useful in calculating the linear absorption coefficient of Al Co Cu Au Fe Pb Ni Pd Pt Ag Ti and W.