Reflection coefficient at a copper boundary

In summary, the reflection coefficient of copper for radio waves at frequency 50Ghz and yellow light (wavelength = 0.6 micrometers) can be calculated using the equation R = E(r)^2/E(I)^2 = (1-n/1+n)^2, where n is the refractive index of copper and is given by n = c/v, where v is the frequency multiplied by the wavelength. However, due to the conductivity of copper, different equations must be used to calculate the refractive index for each frequency.
  • #1
Supra
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Homework Statement



Calculate the reflection coefficient of copper for radio waves at frequency 50Ghz and yellow light (wavelength = 0.6 micrometers)


Homework Equations



Reflection coefficient: R = E(r)^2/E(I)^2 = (1-n/1+n)^2
Where E(r) is the electric intensity of the reflected wave, E(I) is the intensity of the incident wave

Also, refractive index, n, is given by n = c/v, where v is given by frequency x wavelength.

n = (epsilon x mu)^1/2

The Attempt at a Solution



The key variable appears to be the frequency (wavelength for the yellow light) which effects the refractive index of the copper material. My problem is linking the two together, because as stated in the above equations, I am aware of the relationship but can't pin down a definite relationship which allows me to calculate one from the other.

Any attempt to re-arrange n = c/v fails as even if i break v down in frequency x wavelength, i still have 2 unknowns (refractive index and wavelength (for radio waves) and frequency (for yellow light).)

Any help with this would be much appreciated, as once the refractive index is found then the first equation stated can be used.

Many thanks.
 
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  • #2
Copper is a conductor so the problem is much more complicated.
You have to use sigma, the conductivity of copper, and use completely different equations.
 
  • #3
For both of your frequencies, the absorption is negligible, so R=1.
 

Related to Reflection coefficient at a copper boundary

1. What is the reflection coefficient at a copper boundary?

The reflection coefficient at a copper boundary refers to the ratio of the reflected electromagnetic wave to the incident electromagnetic wave at the interface between copper and another material.

2. How is the reflection coefficient at a copper boundary calculated?

The reflection coefficient at a copper boundary can be calculated by taking the square root of the ratio of the conductivity of the incident and reflected materials.

3. What factors affect the reflection coefficient at a copper boundary?

The reflection coefficient at a copper boundary is affected by factors such as the angle of incidence, the dielectric constant of the incident and reflected materials, and the thickness of the copper layer.

4. Why is the reflection coefficient at a copper boundary important?

The reflection coefficient at a copper boundary is important because it determines the amount of energy that is reflected back when an electromagnetic wave encounters a copper surface. This can affect the performance of copper-based electronic devices and circuits.

5. Can the reflection coefficient at a copper boundary be reduced?

Yes, the reflection coefficient at a copper boundary can be reduced by using techniques such as anti-reflective coatings or by adjusting the angle of incidence. It can also be reduced by using materials with similar conductivity and dielectric constants.

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