When a radio wave propagating in one medium impinges upon another medium having different electrical properties, the wave is partially reflected and partially transmitted. If the plane wave is incident on a perfect dielectric, part of the energy is transmitted into the second medium and part of the energy is reflected back into the first medium, and there is no loss of energy in absorption.

lf the second medium is a perfect conductor, then all incident energy is reflected back into the first medium without loss of energy. The electric field intensity of the reflected and transmitted waves may be related to the incident wave in the medium of origin through the Fresnel reflection coefficient $(\Gamma)$. The reflection coefficient is a function of the material properties, and generally depends on the wave polarization, angle of incidence, and the frequency of the propagating wave.

Reflection from dielectrics:

Figure shows an electromagnetic wave incident at an angle $\theta_i$ 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 $\theta_r$, and part of the energy is transmitted (refracted) into the second media at an angle $\theta_t$ . The nature of reflection varies with the direction of polarization of the E-field. The behaviour for arbitrary directions of polarization can be studied by considering the two distinct cases shown in Figure

The plane of incidence is defined as the plane containing the incident, reflected, and transmitted rays. In Figure the E-field polarization is parallel with the plane of incidence (that is, the Efield has a vertical polarization, or normal component, with respect to the reflecting surface) and in Figure 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).

Because of superposition, only two orthogonal polarizations need be considered to solve general reflection problems. The reflection coefficients for the two cases of parallel and perpendicular E field polarization at the boundary of two dielectrics are given by

$$\Gamma_{ \|}=\frac{E_{r}}{E_{i}}=\frac{\eta_{2} \sin \theta_{t}-\eta_{1} \sin \theta_{i}}{\eta_{2} \sin \theta_{t}+\eta_{1} \sin \theta_{i}} \quad \text {(E-field in plane of incidence)}$$

$$\Gamma_{\perp}=\frac{E_{r}}{E_{i}}=\frac{\eta_{2} \sin \theta_{i}-\eta_{1} \sin \theta_{t}}{\eta_{2} \sin \theta_{i}+\eta_{1} \sin \theta_{t}} \text {(E-field normal to the plane of incidence)}$$

Where $\eta$ is the intrinsic impedance of the respective medium

OR

$$\Gamma_{ \|}=\frac{-\varepsilon_{r} \sin \theta_{i}+\sqrt{\varepsilon_{r}-\cos ^{2} \theta_{i}}}{\varepsilon_{r} \sin \theta_{i}+\sqrt{\varepsilon_{r}-\cos ^{2} \theta_{i}}}$$

$$\Gamma_{\perp}=\frac{\sin \theta_{i}-\sqrt{\varepsilon_{r}-\cos ^{2} \theta_{i}}}{\sin \theta_{i}+\sqrt{\varepsilon_{r}-\cos ^{2} \theta_{i}}}$$

Where $\varepsilon$ is the permittivity of the respective medium