Question

A plane electromagnetic wave propagating in z-direction is incident on the boundary between two linear dielectric media. The boundary is in the x-y plane perpendicular to the direction of propagation of the wave. Using the boundary conditions on the electric and magnetic fields associated with the wave, show that if the incident wave is plane polarised then the reflected and transmitted waves also have the same polarisation.

20 Feb 2025
Answer :
Word Count : 607

In the context of classical electrodynamics, when an electromagnetic wave propagates and interacts with a boundary between two dielectric media, the behavior of the electric and magnetic fields can be understood by applying the boundary conditions at the interface. We assume that the electromagnetic wave is incident on the boundary between two linear dielectric media, and the wave propagates along the z-axis.

Let the electric and magnetic fields of the incident, reflected, and transmitted waves be denoted as follows:

- Incident wave: \( \mathbf{E}_i \) and \( \mathbf{B}_i \)
- Reflected wave: \( \mathbf{E}_r \) and \( \mathbf{B}_r \)
- Transmitted wave: \( \mathbf{E}_t \) and \( \mathbf{B}_t \)

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