University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

445

Pages:

5
Author:

Jabin F.

Section 1 Equation: ⃗Ei = E0i * ŷ * e^(i(kz - ωt)) Equation: ⃗Ei = E0i * ŷ * e^(i(kiz cosθi + kiy sinθi - ωt)) Equation: ⃗Er = E0r * ŷ * e^(i(-kiz cosθr + kiy sinθr - ωt)) Equation: ⃗Et = E0t * ŷ * e^(i(kiz cosθt + kiy sinθt - ωt)) Boundary condition: Eabove = Ebelow Section 2 Equation: Ei + Er = Et Equation: E0i + E0r = E0t Equation: ki sinθi = ky sinθr = kt sinθt Conclusion: ki = kr (they are in the same plane) Detailed Description The image appears to be a continuation of previous calculations related to electromagnetic waves at a boundary. It focuses on the static relations for incident, reflected, and transmitted waves. Section 1 Introduces the equations for the incident, reflected, and transmitted electric fields. Expresses the wave vectors in terms of their components. Section 2 Applies the boundary condition at the interface. Derives the relationship between the amplitudes of the incident, reflected, and transmitted waves. Derives the relationship between the wave vectors. Concludes that the incident and reflected waves are in the same plane. Section 1 Equations: sinθi = sinθr θi = θr ki sinθi = kt sinθt sinθi / sinθt = kt / ki = vi / vt = n2 / n1 Snell's law Section 2 Equations: ωi = ωr = ωt vi = vr = vt λi = λr = λt