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Does electric perm and magnetic perm give you enough info to work out OD?

Thanks in advance

Thanks in advance

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- Thread starter Andrew Wright
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In summary, when a substance is subject to a variable external field, its polarization, for one, does not obey the same proportionality factors as applied to constant field. For another, just adjusting the real permittivity values does not suffice, because the polarization turns out to depend on the past history of external field (though fortunately not of its future...).

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Does electric perm and magnetic perm give you enough info to work out OD?

Thanks in advance

Thanks in advance

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Do you think I have got the right forum for this topic?

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I'm not sure to which physical situation you are referring to. I guess you mean that you neglect the imaginary part of the permittivity and then you have [EDIT: Corrected obvious typo in the final equation]

$$c=\frac{1}{\sqrt{\epsilon \mu}}=\frac{1}{\sqrt{\epsilon_0 \mu_0 \epsilon_{r} \mu_{r}}}=c_0/n \; \Rightarrow \; n=\sqrt{\epsilon_r \mu_r}.$$

$$c=\frac{1}{\sqrt{\epsilon \mu}}=\frac{1}{\sqrt{\epsilon_0 \mu_0 \epsilon_{r} \mu_{r}}}=c_0/n \; \Rightarrow \; n=\sqrt{\epsilon_r \mu_r}.$$

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Cool :) Thanks.

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Note the correction of the obvious typo! It's, of course,

$$n=\sqrt{\epsilon_r \mu_r}.$$

$$n=\sqrt{\epsilon_r \mu_r}.$$

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Is refractive index the same as optical density?

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https://en.wikipedia.org/wiki/Refractive_index#Complex_refractive_index

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https://sciencing.com/difference-between-optical-density-absorbance-7842652.html

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vanhees71 said:As far as I know "optical density" is an oldfashioned expression for the absorption coefficient, i.e., it's rather related to the imaginary part of the refractive index, the extinction coefficient

And in fact the designation survives in nomenclature for "neutral density" attenuating optical filters.

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Andrew Wright said:Summary::Hi. Is there a formula for getting OD from electric permativity and magnetic permeability?

Does electric perm and magnetic perm give you enough info to work out OD?

Thanks in advance

If I understand you correctly, 'yes'- most simply, the permittivity ε and permeability μ must be complex-valued. Optical density is associated with absorption (or scattering)- a scattering medium is heterogeneous, so in that case the refractive index may be real-valued but there is not a single-valued ε or μ for the entire sample.

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...there is not a single-valued ε or μ for the entire sample.

Does this mean the perms have different values at different wavelengths?

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Yes!

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In the usual approximation you consider visible light and usual matter. The typical extension of an atom is much smaller than the wave length and thus you can treat the matter as homogeneous and that's why the permittivity and permeability can be considered as frequency dependent only (in the frequency domain). For a nice treatment in terms of classical physics, see e.g., the Feynman Lectures. The phenomenology is amazingly pretty accurate though of course the "true theory" is quantum mechanics:

https://www.feynmanlectures.caltech.edu/II_32.html

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Andrew Wright said:Does this mean the perms have different values at different wavelengths?

They can- that's called 'dispersion'. But different materials have different ε(λ) and μ(λ) as well. Discontinuities at material boundaries leads to scattering, which is not the same as absorption. OD is often used as a way to characterize turbid media.

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When a substance is subject to static electric and magnetic fields, its polarization is proportional to the present (constant!) applied field.Andrew Wright said:

But when the substance is subject to a variable external field, its polarization, for one, does not obey the same proportionality factors as applied to constant field. For another, just adjusting the real permittivity values does not suffice, because the polarization turns out to depend on the past history of external field (though fortunately not of its future...), even for the same values of external field.

Compare a current circuit - the mathematics of electromagnetic waves is actually somewhat analogical to current circuits!

In direct current circuits, resistors have a fixed and positive resistance, and current always flows in the direction of voltage.

In alternsting current circuits, however, resistance is no longer constant, or even required to be positive: an inductive coil can support current against voltage for some time after voltage reverses.

Many simple alternating current circuits can be approached as having complex resistance, though. (Many cannot!)

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That's fascinating. Thank you :)

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