An electromagnetic wave emitter makes an obliquely incident from the air on the surface of a...

 

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An electromagnetic wave emitter makes an obliquely incident from the air on the surface of a liquid with refractive index n √2 a linearly polarized uniform plane wave with average power density = 12 mW/m2 and frequency f = 7.2 GHz. For the analysis, a system is considered of coordinates P av (20, ), TT 7πt 4' = such that the liquid occupies the half-space z <0 and the emitter is located at the point P₁ in spherical coordinates, with the radius in centimeters. The wave vector and the electric field of the emitted wave respectively follow the direction of the unit spherical vectors and - seen from the point P₁. It is requested: 1 a) The Cartesian coordinates of the point P b) The unit vectors that give the direction of the electric field and that of the wave vector of the incident wave on the liquid (e, k) as a function of Cartesian unit vectors (x, y, z); c) Reason what the plane of incidence (PI) will be in this case, describe it using graphical representations and find the normal unit vector to this plane (u) as a function of Cartesian unit vectors; d) The unit vector that gives the direction of the magnetic field (h): as a function of spherical vectors seen from the point P, and as a function of Cartesian unit vectors; 1 e) The angles of incidence, reflection and transmission referred to the normal direction to the surface of the liquid following the usual convention in incidence problems (0i, Or, Ot); f) The unit wave vectors of the reflected and transmitted waves kk. In the following sections, complete phasor expressions are requested as a function of unit vectors and Cartesian coordinates of g) The electric and magnetic fields associated with the incident wave, respectively E₁ (z > 0), H₂ (z > 0); h) The electric fields associated with the reflected and transmitted waves, respectively Ē, (z > 0), E, (z < 0). An electromagnetic wave emitter makes an obliquely incident from the air on the surface of a liquid with refractive index n √2 a linearly polarized uniform plane wave with average power density = 12 mW/m2 and frequency f = 7.2 GHz. For the analysis, a system is considered of coordinates P av (20, ), TT 7πt 4' = such that the liquid occupies the half-space z <0 and the emitter is located at the point P₁ in spherical coordinates, with the radius in centimeters. The wave vector and the electric field of the emitted wave respectively follow the direction of the unit spherical vectors and - seen from the point P₁. It is requested: 1 a) The Cartesian coordinates of the point P b) The unit vectors that give the direction of the electric field and that of the wave vector of the incident wave on the liquid (e, k) as a function of Cartesian unit vectors (x, y, z); c) Reason what the plane of incidence (PI) will be in this case, describe it using graphical representations and find the normal unit vector to this plane (u) as a function of Cartesian unit vectors; d) The unit vector that gives the direction of the magnetic field (h): as a function of spherical vectors seen from the point P, and as a function of Cartesian unit vectors; 1 e) The angles of incidence, reflection and transmission referred to the normal direction to the surface of the liquid following the usual convention in incidence problems (0i, Or, Ot); f) The unit wave vectors of the reflected and transmitted waves kk. In the following sections, complete phasor expressions are requested as a function of unit vectors and Cartesian coordinates of g) The electric and magnetic fields associated with the incident wave, respectively E₁ (z > 0), H₂ (z > 0); h) The electric fields associated with the reflected and transmitted waves, respectively Ē, (z > 0), E, (z < 0).

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An electromagnetic wave emitter makes an obliquely incident from the air on the surface of a liquid with refractive index n squaeroot of 2 a linearly polarized uniform plane wave with average power de... View the full answer