1 A monochromatic (628 nm), homogeneous plane wave propagates in a dielectric material of electric permittivity &₁ = 980 and magnetic permeability f1 40. The amplitude of the electric field that describes this incident wave is 100 (V m-¹). The wave propagates in the z-direction and is linearly polarised in the x-direction. (a) By comparing with the general form of the electric field describing a plane wave, write down the specific form of the electric field that describes the wave.
1 A monochromatic (628 nm), homogeneous plane wave propagates in a dielectric material of electric permittivity &₁ = 980 and magnetic permeability f1 40. The amplitude of the electric field that describes this incident wave is 100 (V m-¹). The wave propagates in the z-direction and is linearly polarised in the x-direction. (a) By comparing with the general form of the electric field describing a plane wave, write down the specific form of the electric field that describes the wave.
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parts (a), (b), (c) please
Transcribed Image Text:A monochromatic (628 nm), homogeneous plane wave propagates in a
dielectric material of electric permittivity ₁ = 90 and magnetic permeability
₁ = 40. The amplitude of the electric field that describes this incident wave is
100 (V m-¹). The wave propagates in the z-direction and is linearly polarised in
the x-direction.
(a) By comparing with the general form of the electric field describing a plane
wave, write down the specific form of the electric field that describes the wave.
1
(b) Starting with B = − k × Ē, where w is the angular frequency, and is the
propagation vector, deduce the specific form of the magnetic field describing
the wave.
(c) Calculate the divergence and the curl of the electric field vector.
(d) Deduce the specific form of the Poynting vector describing the magnitude and
direction of the flow of energy.
(e) The wave is normally incident on a second dielectric material of electric
permittivity 2 = 40 and magnetic permeability 2 = 40 (as illustrated
in the figure below).
Medium 1
(&₂, H₂)
Medium 2
(&₂, H₂)
Incident
electromagnetic
Transmitted
electromagnetic
wave
wave
(i) Calculate the reflection and the transmission coefficients as fractions of
intensities at the interface between the two media.
(ii) Calculate the propagation constant in the second medium.
(iii) Write an expression for the electric field describing the propagation of
the wave in the second medium.
Z
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