Talk:Penetration depth

Questions posed by Fd97207

I think there is a problem with this formula. I think its only valid in the radio to microwave range. Per this formula, gamma waves should get strongly attenuated as they pass through a material. But they don't. People say gamma rays are more energetic, and the way to counter this argument is to consider a radio source and a gamma source of equal intensity (the radio source will have many more photons in it). Also I know that the refractive index varies with frequency, but its mostly real, and the frequency dependence is not so wild, so as to make the overall formula give large value of penetration for a gamma wave. If someone can clear this up, and explain the frequency range in which this formula is valid, and why, that would be great.Fd97207 (talk) 19:05, 16 March 2011 (UTC)

Hi, I contributed significantly to both this and the skin effect articles and will defend the contents thereof. Yes, penetration depth (as it SAYS in the article) IS the same as skin depth, except for a factor of 2 depending on definition applied to 1/e intensity or 1/e amplitude. Now which formula do you have a "problem" with? There aren't any specific formulas in this article that go beyond the definition of δ. There are in the skin effect article, and the range of validities is very well spelled out. In particular it says that the formulas presented for conductors are only valid well below the plasma frequency, so gamma rays obviously don't apply. δ for metals at gamma ray frequencies applies as much as for any others: if the gamma rays don't get attenuated much (as they don't) then δ will be very large. The relation of δ to the imaginary part of n is also basically a matter of definition. In particular, n at gamma ray (and xray) frequencies is almost exactly 1. So I don't understand your problem, and if you want to ask provocative questions, please first demonstrate that you have actually read the articles in question. Interferometrist (talk) 21:05, 16 March 2011 (UTC)

This question:Isn't this the same as the skin depth? wasn't asked by me. Someone put this in, without signing their name. I am going to delete it. Now, let's leave out conductors and consider dielectrics. The formula in question is penetration depth or attenuation constant as they are basically interchangeable. I have never seen the formula being used for waves beyond microwave range. Indeed, it predicts attenuation increases with frequency which is not true considering behavior of gamma rays. So I am asking, If someone can clear this up, and explain the frequency range in which this formula is valid, and why, that would be great.Fd97207 (talk) 04:25, 17 March 2011 (UTC)

Listen, you are simply mistaken. It's all right: this isn't taught in college physics much, but the refractive index does NOT monotonically increase, let alone the imaginary part which is all that concerns us here. In a dielectric f you look at n it rises UNTIL it gets near a resonance, if the resonance were totally sharp it would rise to infinity and come back from -infinity rising again, but at a lower plateau than where it was. By the time you get way into the UV or xray, it has passed all the resonances and settled to 1. Well away from resonances, the attenuation is small and delta can be huge. It depends on the atom's energy levels, broadening, collisions, etc.

For metals, their n is approx N*(1-j) with N decreasing with optical frequency but this approx gets worse in the near IR or visible and it should: in the UV you hit the plasma frequency where n becomes >0 with a considerable imaginary part, less so for good conductors. Also now the electrons are limited by inertia, not collisions. As frequency increases, the effect of atoms (electrons) diminishes and becomes 1 at xrays. Of course lead will block gamma rays due to its nucleus etc. Anyway, n changes radically especially in metals over frequency, and the relationship alpha = Im(n) holds regardless, so please don't get so upset because you expected something different, ok? Interferometrist (talk) 04:53, 17 March 2011 (UTC)

To rephrase Interferometrist: The formula is ${\frac {1}{\delta _{e}}}={\frac {\omega }{c}}\;\mathrm {Im} ({\tilde {n}})$. You might think from this formula, as $\omega$ gets larger and larger, $\delta _{e}$ gets smaller and smaller. But that's not right because $\mathrm {Im} ({\tilde {n}})$ is also a function of $\omega$. Actually, $\mathrm {Im} ({\tilde {n}})$ decreases to zero at large $\omega$ (e.g. gamma rays), and becomes so small that it more than makes up for the increase in $\omega$. Maybe it would be clearer if it were written $\mathrm {Im} ({\tilde {n}}(\omega ))$ in the equation, to emphasize that it is a function of $\omega$. --Steve (talk) 06:23, 17 March 2011 (UTC)

Thanks Steve, I think you got to the nub of the confusion and laid it out while I was sort of rambling on.... And in fact I will NOW edit the article to make it more clear that refractive index is very much a function of frequency, and has an imaginary part. Since, come to think of it, it's taught in optics as being approximately constant, and if you read the fine print you learn it varys by 1 or 2% over the visible range, (and no mention of its imaginary part!) and one could easily be led to the wrong conclusions about far different frequencies. I'll change it now, but if you have any better wording, do change it. This article shouldn't get into the reason that n changes, but should point it out. Interferometrist (talk) 12:23, 17 March 2011 (UTC)