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Reflection and Refraction of Plane Electromagnetic Waves at The Interface Between Two Dielectrics

When a plane wave propagating in a homogenous medium encounters an interface with a different medium, a portion of the wave is reflected from the interface while the remainder of the wave is transmitted. The reflected and transmitted waves can be determined by enforcing the fundamental electromagnetic field boundary conditions at the media interface. The proportion of reflection and transmission depends on the constitutive parameters of the media, i.e., ε, μ, σ.

Here, we consider the reflection and refraction of a plane wave incident on a single boundary separating two different dielectric media. Two types of incidence may occur:
  1. Normal incidence
  2. Oblique incidence

Oblique Incidence

Any plane wave which is obliquely incident on a planar media interface can be represented by a linear combination of two special cases:
  1. Perpendicular or Horizontal Polarisation
     
    When the electric field vector Description: 19727.png is perpendicular to the plane of incidence, i.e., the electric vector is parallel to the boundary surface, it is called perpendicular or horizontal polarisation.
     
    Figure: illustrates a perpendicularly polarised wave.
Description: 30978.png
Perpendicular polarisation
  1. Parallel or Vertical Polarisation
     
    When the electric field vector Description: 22382.png is parallel to the plane of incidence, i.e., the magnetic field is parallel to the boundary surface, it is called parallel or vertical polarisation.
     
    Figure: illustrates a parallel polarised wave.
Description: 31085.png
Parallel polarisation

Reflection and Transmission Coefficients for Perpendicular and Parallel Polarisation

We consider the figure below.
Description: 31145.png
 Reflection and transmission of plane waves
 
​For the figure, the plane of the paper is the plane of incidence. The figure shows two rays of the EM wave:
 
 
Ray 1: reflected along AE, transmitted along AD
 
 
Ray 2: reflected along BG, transmitted along BF

The directions:
 
AE and BG are parallel
 
AD and BF are parallel

The line AC which is perpendicular to the incident rays represents the equiphase surface in the medium 1.
 
The line DB which is perpendicular to the transmitted rays represents the equiphase surface in the medium 2.
  • Ray 1 travels the distance AD,
  • Ray 2 travels the distance CB, and
  • Reflected Ray 1 travels the distance AE.
The time taken is the same for all three distances.
 
Description: 18409.png

This equation is termed Snell’s law.
 
Note: The plane of incidence is the plane containing the incident wave and the normal to the interfacing surface.
 
The angle of incidence is defined as the angle between the direction of propagation and the normal to the boundary.
 
The terms ‘horizontally’ and ‘vertically’ polarised wave refer to the fact that the waves from horizontal and vertical antennas, respectively, would produce these particular orientations of electric and magnetic vectors in waves striking the surface of the earth.





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