- #1
- 2,810
- 604
I've got a problem asking for the reflection coefficient of a system consisting of a ideal conductor covered with a thin layer of lossless dielectric. I just don't know what to do.How can I do it?
Thanks
Thanks
DrDu said:The system is neither absorbing nor transmitting. Methinks that therefore the reflectivity has to be 100%.
Shyan said:How can I prove those?
I mean, I know the physical reasoning, but it looks like some calculation is demanded because in the problem the width of the dielectric layer is given as a parameter [itex] \tau [/itex] and it is stated explicitly to "calculate" the coefficient!
Born2bwire said:This is a three layer system and the reflection coefficient will reflect the various phase changes and guided modes that can arise.
Shyan said:How can I prove those?
I mean, I know the physical reasoning, but it looks like some calculation is demanded because in the problem the width of the dielectric layer is given as a parameter [itex] \tau [/itex] and it is stated explicitly to "calculate" the coefficient!
Born2bwire said:This is a three layer system and the reflection coefficient will reflect the various phase changes and guided modes that can arise. Did the problem specify a specific polarization and direction of the wave?
The general solution can be found in texts like Balanis' on EM or Chew's "Waves and Fields in Inhogeneous Media.' Balanis is the more accessible text.
Is the layer thickness on the order of the wavelength? There could be a simplification if this is a problem of optical light off of a coated metal compared to the RF case of plane waves in layered media.
DrDu said:Usually, the starting point would be to set up the incoming and outgoing waves in the different layers and specify the boundary conditions. It is crucial that in the third layer, there is only an incoming wave, but no outcoming wave.
So you can work backward from there.
In your problem, there is not even an incoming wave in the third layer, so nontrivial effects are only to be expected if the second layer is absorbing, which you explicitly excluded.
That's what I said.Shyan said:The third layer is an ideal conductor, so no wave is present in it, neither an incoming wave nor an outgoing one!
No, E will be zero at the boundary 2/3 but not inside all of 2. You will get a standing wave and in a standing wave, E and B will be 90 degrees out of phase. So there will be a nonvanishing oscillating B at the boundary and away from the boundary E will be non-zero due to rot E= dB/dtAs a boundary condition, the tangential component of the electric field should be continuous at the interface. Because here the third layer is an ideal conductor, the electric field, and so its tangential component, is zero inside it and so the tangential component of the electric field should be zero at the second layer too. But for normal incidence, we only have tangential components of fields which means the field is zero in the second layer!
!
Shyan said:In fact the problem asks for the reflection coefficient for the normal incidence which makes both polarizations the same!
Nothing is assumed about the layer's thickness.
The third layer is an ideal conductor, so no wave is present in it, neither an incoming wave nor an outgoing one!
As a boundary condition, the tangential component of the electric field should be continuous at the interface. Because here the third layer is an ideal conductor, the electric field, and so its tangential component, is zero inside it and so the tangential component of the electric field should be zero at the second layer too. But for normal incidence, we only have tangential components of fields which means the field is zero in the second layer!
Also we should note that there will be infinite number of reflections until the wave is reflected completely. But this point should be considered after solving the previous one!
This problem is from a bunch of problems from previous years physics olympiads. I mean national olympiad or meyabe a level behind that!I'm still wondering if this is really the problem you are being asked as it seems like it's rather advanced from what you have stated. I could imagine that they were asking for the reflectivity which as already been stated is a trivial 100% assuming lossless dielectrics.
The reflection coefficient is a measure of the amount of energy reflected by a material when a wave of energy, such as light or sound, is incident upon it. It is typically represented by the symbol "R" and is expressed as a fraction or percentage.
The reflection coefficient is calculated by dividing the amount of energy reflected by the total amount of incident energy. This can be expressed mathematically as R = (reflected energy / incident energy). The resulting value ranges from 0 to 1 or 0% to 100%, with higher values indicating a greater amount of energy being reflected.
The reflection coefficient is influenced by various factors, including the properties of the material, the angle of incidence, and the wavelength of the incident wave. Materials with a higher refractive index tend to have a higher reflection coefficient, while materials with a lower index have a lower coefficient. The angle of incidence also plays a significant role, as higher angles usually result in a higher reflection coefficient. Additionally, the wavelength of the incident wave can affect the reflection coefficient, as some materials have different reflective properties for different wavelengths.
The reflection coefficient is used in many practical applications, including optics, acoustics, and electronics. In optics, it is used to determine the amount of light reflected by a surface, which can be important for designing optical systems. In acoustics, the reflection coefficient is used to characterize the reflective properties of materials, which is important for noise control and room acoustics. In electronics, the reflection coefficient is used to measure the impedance match between components, which is essential for efficient signal transmission.
No, the reflection coefficient cannot be greater than 1. A value greater than 1 would indicate that more energy is being reflected than is being incident, which is not physically possible. The maximum value for the reflection coefficient is 1 or 100%, which would indicate total reflection of the incident energy.