An EM field is normally incident on a slab with relative permittivity 4 and rela

Question

An EM field is normally incident on a slab with relative permittivity 4 and relative permeability 1. Assume that the incident E & H fields are both 1 (you can use relative units for all that follows). (a) What is the refractive index and the impedance of this material relative to free space? (b) Using the equations for Fresnel coefficients and the impedance, determine the transmitted E & H fields (c) Using physical arguments (not the Fresnel coefficients), determine the magnitude and phase of the reflected fields.

Explanation / Answer

Refractive index is approximately equal to under root of relative permittivity of that medium so, RI ~ 2.

And impedence ~{ permiability/permittivity}1/2. = 1/2 or 0.5.

(B) As incedence angle is 90degrees or normal incidence,

Transmission coefficient= 2*Z2/Z1+Z2.

=> 2×0.5/1+0.5 = 1/1.5 = 0.67.

(C) Total probability of certain distribution is always 1.

when 0.67 is transmitted, obviously reflections take 0.33part of it.

And phase shift of 180degrees is explained by principle of superposition, as at the interface, amplitude is zero and so amplitude of reflected and incoming wave should be zero at point of interface this is only possible when there is a phase shift of 180degrees.

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