# 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.,*Îµ*, Î¼,

*Ïƒ*.

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:

- Normal incidence
- 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:*Perpendicular or Horizontal Polarisation**When the electric field vector 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.*

â€‹

**Perpendicular polarisation**

*Parallel or Vertical Polarisation**When the electric field vector 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.*

â€‹

**Parallel polarisation**

# Reflection and Transmission Coefficients for Perpendicular and Parallel Polarisation

We consider the figure below.

â€‹

**Reflection and transmission of plane waves**

â€‹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.

âˆ´ | |

âˆ´ | |

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This equation is termed

*Snellâ€™s law*.

**Note:**The

*plane of incidence*is the plane containing the incident wave and the normal to the interfacing surface.

The
The terms

*angle of incidence*is defined as the angle between the direction of propagation and the normal to the boundary.*â€˜horizontallyâ€™*and*â€˜verticallyâ€™*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.