Wave Propagation and Interface Behavior Quiz

When a plane wave hits a boundary between two materials at an angle, it behaves similarly to normal incidence. Part of the wave passes through (transmitted) and part of it bounces back (reflected). The way the wave acts at the boundary depends on its polarization.

Snell's Law describes the relationship between the angle of incidence, angle of refraction, and the refractive indices of the two materials. It determines how much the wave bends as it passes from one material to another.

The critical angle is the angle of incidence at which the refracted wave travels along the boundary between the two materials. Beyond this angle, there is only reflection and no transmission.

In oblique incidence, there are two polarization types: parallel and perpendicular. Parallel polarization means the electric field is parallel to the plane of incidence, while in perpendicular polarization, the electric field is perpendicular to the plane of incidence.

The Brewster angle is the specific angle of incidence where the reflected wave is completely polarized with its electric field perpendicular to the plane of incidence. This means no parallel polarized light is reflected.

The direction of propagation of a wave, represented by a vector.

The unit vector representing the direction of propagation of a wave, obtained by dividing the propagation vector by its magnitude.

The angle between the incident wave and the normal line to the boundary.

The angle between the reflected wave and the normal line to the boundary.

The component of the propagation vector in the x-direction.

The component of the propagation vector in the z-direction.

The magnitude of the propagation vector, representing the wave's speed in a specific medium.

The component of the incident wave's propagation vector in the z-direction.

Describes the direction of propagation of a wave. It is a vector quantity with components in the x, y, and z directions.

The plane formed by the direction of the incident wave (𝐤𝑖) and the normal vector to the surface at the point of incidence.

The electric field vector is parallel to the plane of incidence. This means the electric field oscillates in the plane defined by the incident wave direction and the surface normal.

The electric field vector is perpendicular to the plane of incidence. This means the electric field oscillates perpendicular to the plane defined by the incident wave direction and the surface normal.

The wave number or propagation constant, k, is a measure of how many waves occur in a given distance (usually in radians per meter).

The phase constant, β, is a measure of the phase change of a wave per unit distance. For lossless media, it is equal to the wave number.

Describes the relationship between the electric field (E), magnetic field (H), and the direction of wave propagation (k). The Poynting vector is proportional to the cross product of E and H.

The ratio of the electric field intensity to the magnetic field intensity in a medium.

The angle between the incident wave and the normal to the boundary between two materials.

The angle between the reflected wave and the normal to the boundary between two materials.

The angle between the transmitted wave and the normal to the boundary between two materials.

The time-averaged Poynting vector represents the average power density of an electromagnetic wave. It's a vector quantity and provides information about the direction and magnitude of power flow.

The time-averaged Poynting vector for a plane wave traveling in a lossless medium is calculated as the real part of the cross product of the electric and magnetic field vectors.

The power density is the amount of power per unit area, and in this context, it represents the intensity of the electromagnetic wave.

The unit of power density is Watts per square meter (W/m²).

The wave impedance (η) is a property of the medium that the electromagnetic wave is traveling through and influences the relationship between the electric and magnetic fields. It's a complex quantity in general.

The time-averaged Poynting vector is proportional to the square of the electric field magnitude and inversely proportional to the square of the wave impedance.

The polarization of an electromagnetic wave refers to the orientation of the electric field vector. When the electric field is parallel to the plane of incidence, it's called parallel polarization.

The transmission coefficient (𝜏⊥) represents the fraction of the incident electric field that is transmitted into the second medium for perpendicular polarization.

The reflection coefficient (Γ⊥) represents the fraction of the incident electric field that is reflected back into the first medium for perpendicular polarization.

The equation 1 + Γ⊥ = 𝜏⊥ describes the conservation of energy at the boundary. The sum of the transmitted and reflected power equals the incident power.

The transmission coefficient (𝜏⊥) can be expressed in terms of the angles of incidence (𝜃𝑖) and the refractive indices of the two media (𝜂1 and 𝜂2) using Snell's law.

The time-averaged power density transmitted into the second medium is calculated by multiplying the square of the transmitted electric field amplitude by the impedance of the second medium and dividing by 2.

The relative permittivity (𝜀𝑟) and relative permeability (𝜇𝑟) of a material determine its refractive index and, therefore, its effect on the transmission and reflection of light.

The perpendicular polarization refers to the case where the electric field of the light wave is perpendicular to the plane of incidence, which is defined by the incident ray and the normal to the boundary.