# Reflexión electromagnética/Índice/Reflexión de los Dieléctricos

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# Reflexión de los Dieléctricos

En la reflexión dieléctrica se muestra una onda incide con un ángulo ${\displaystyle \theta _{i}}$, con el plano limite entre dos medios dieléctricos frontera, donde parte de la energía se refleja de regreso al primer medio en un ángulo ${\displaystyle \theta _{r}}$ y otras transmite con ${\displaystyle \theta _{t}}$.

Plano incidente: se define como el plano en el que se encuentran la onda incidente, reflejada y transmitida

En la figura 3.4 se puede observar que, el campo eléctrico se encuentra polarizado de forma paralela al plano incídete en la figura 3.4.a, y la polarización del campo eléctrico es perpendicular al plano incidente en la 3.4.b.

Los parámetros ${\displaystyle \epsilon _{1}}$, ${\displaystyle \mu _{1}}$, ${\displaystyle \sigma _{1}}$ y ${\displaystyle \epsilon _{2}}$, ${\displaystyle \mu _{2}}$, ${\displaystyle \sigma _{2}}$ representan la permitividad, la permeabilidad y la conductividad respectivamente.

La constante dieléctrica de un dieléctrico perfecto esta relacionada con un valor relativo ${\displaystyle \epsilon _{r}}$ y ${\displaystyle \epsilon _{0}}$ tal que ${\displaystyle \epsilon }$ ${\displaystyle =}$ ${\displaystyle \epsilon _{r}*\epsilon _{0}}$ es la permitividad del vacío siendo ${\displaystyle 8.85*10^{-12}}$ ${\displaystyle {\frac {F}{m}}}$.

# Reflection from Dielectrics

Figure 3.4 shows an electromagnetic wave incident at an angle ${\displaystyle \theta _{i}}$, with the plane of the boundary between two dielectric media. As shown in the figure, part of the energy is reflected back to the first media at an angle ${\displaystyle \theta _{r}}$, and part of the energy is transmitted (refracted) into the second media at an angle ${\displaystyle \theta _{t}}$,. The nature of reflection varies with the direction of polarization of the E-field. The behavior for arbitrary directions of polarization can be studied by considering the two distinct cases shown in Figure 3.4. The plane of incidenceis defined as the plane containing the incident, reflected, and transmitted rays [Ram65]. In Figure 3.4a, the E-field polarization is parallel with the plane of incidence (that is, the E-field has a vertical polarization, or normal component, with respect to the reflecting surface) and in Figure 3.4b, the E-field polarization is perpendicular to the plane of incidence (that is, the incident E-field is pointing out of the page towards the reader, and is perpendicular to the page and parallel to the reflecting surface).
In Figure 3.4, the subscripts i, r, t refer to the incident, reflected, and transmitted fields, respectively. Parameters ${\displaystyle \epsilon _{1}}$, ${\displaystyle \mu _{1}}$, ${\displaystyle \sigma _{1}}$ y ${\displaystyle \epsilon _{2}}$, ${\displaystyle \mu _{2}}$, ${\displaystyle \sigma _{2}}$, represent the permittivity, permeability, and conductance of the two media, respectively. Often, the dielectric constant of a perfect (lossless) dielectric is related to a relative value of permittivity, ${\displaystyle \epsilon _{r}}$, such that ${\displaystyle \epsilon =\epsilon _{0}*\epsilon _{r}}$ where ${\displaystyle \epsilon _{0}}$ is a constant given by ${\displaystyle 8.85x10^{-12}}$ ${\displaystyle {\frac {F}{m}}}$. If a dielectric material is lossy, it will absorb power and may be described by a complex dielectric constant given by

${\displaystyle \epsilon =\epsilon _{0}*\epsilon _{r}-j\epsilon _{'}}$

where,

${\displaystyle \epsilon _{'}={\frac {\sigma }{2*\pi *f}}}$

and ${\displaystyle \sigma }$ is the conductivity of the material measured in Siemens/meter. The terms ${\displaystyle \epsilon _{r}}$ and ${\displaystyle \sigma }$ are generally insensitive to operating frequency when the material is a good conductor (${\displaystyle f<\sigma )/(\epsilon _{0}\epsilon _{r}}$) ). For lossy dielectrics, ${\displaystyle \epsilon _{r}}$ and ${\displaystyle \epsilon _{r}}$ are generally constant with frequency, but ${\displaystyle \sigma }$ may be sensitive to the operating frequency, as shown in Table 3.1. Electrical properties of a wide range of materials were characterized over a large frequency range by Von Hipple [Von54]