# Reflectance of metals at low frequencies

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• nmbr28albert
In summary, the Drude model predicts a purely imaginary dielectric constant and absorption coefficient for metals in the low frequency regime. However, when comparing this to actual reflectivities of metals in the infrared, the reflectance is almost 100%, which may suggest a shortcoming in the Drude model. This is due to the large and/or imaginary value of the index of refraction, resulting in most of the incident light being reflected rather than absorbed.
nmbr28albert
When calculating the dielectric constant of metals using the Drude model, in the low frequency regime (infrared and beyond) one gets an approximately pure imaginary value:
$$\epsilon(\omega) \approx i\frac{4\pi n e^2\tau}{m_e\omega}$$
which gives an absorption coefficient:
$$\alpha(\omega) \approx \frac{\omega}{c}\sqrt{\frac{8\pi ne^2\tau}{m_e\omega}}$$
When looking at graphs of actual reflectivities of metals in the infrared, the reflectance is almost 100%. From this result however, I first thought that most of the incident light would be absorbed rather than reflected. Is there a physical reason for this difference, or is this a shortcoming of the Drude model?

The reflectivity ## R ## at normal incidence is given by ## R=|(n-1)|^2/|(n+1)|^2 ##. When ## n ## is large and/or has a large imagninary part, the calculated ## R ## is very nearly 1.0. (The index ## n ## can be computed from ## \epsilon ## : ## n=\sqrt{\epsilon} ## ). Whatever gets inside the metal does not propagate very far, but very little gets inside. Most of it gets reflected.

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nmbr28albert

## What is the reflectance of metals at low frequencies?

The reflectance of metals at low frequencies refers to the amount of light that is reflected off of a metal surface when it is exposed to electromagnetic radiation with a low frequency, such as radio waves or microwaves.

## Why is the study of reflectance of metals at low frequencies important?

The study of reflectance of metals at low frequencies is important because it can provide insights into the properties of metals and how they interact with electromagnetic radiation. This information is useful for a variety of applications, such as in the development of communication technologies and the design of energy-efficient materials.

## How is the reflectance of metals at low frequencies measured?

The reflectance of metals at low frequencies is typically measured using a spectrophotometer, which measures the amount of light reflected off of a metal surface at different frequencies. This data can then be used to calculate the reflectance of the metal at a specific frequency.

## What factors can affect the reflectance of metals at low frequencies?

The reflectance of metals at low frequencies can be affected by a variety of factors, including the type of metal, the surface finish of the metal, and the angle at which the radiation hits the metal surface. Additionally, the presence of impurities or coatings on the metal can also impact its reflectance.

## How does the reflectance of metals at low frequencies differ from that at high frequencies?

The reflectance of metals at low frequencies is typically lower than that at high frequencies. This is because at low frequencies, the radiation is not energetic enough to cause significant electron movements in the metal, resulting in lower reflectance. At higher frequencies, the radiation has more energy and can cause a greater number of electrons to move, leading to higher reflectance.

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