IGNOU MPH 7 2026 - Using boundary conditions on the electric and magnetic fields, derive

Question

Using boundary conditions on the electric and magnetic fields, derive the Fresnel reflection and transmission coefficients for a plane wave incident normally on a boundary between two dielectric media.

19 Jan 2026

Answer :

Word Count : 481

Consider a uniform plane electromagnetic wave incident normally on a planar boundary separating two homogeneous, isotropic, non-conducting dielectric media. Let medium 1 (z < 0) be characterized by permittivity ε₁, permeability μ₁, refractive index n₁, and intrinsic impedance η₁ = √(μ₁/ε₁). Medium 2 (z > 0) is characterized similarly by ε₂, μ₂, n₂, and η₂. The incident wave propagates along the +z direction with its electric field polarized along the x-axis and magnetic field along the y-axis. The electric field of the incident wave can be written as Eᵢ = E₀ᵢ e^{i(k₁z − ωt)} x̂, where k₁ is the wave number in medium 1. At the boundary z = 0, part of the wave is reflected back into medium 1 and part is transmitted into medium 2. The reflected electric field is Eᵣ = E₀ᵣ e^{i(−k₁z − ωt)} x̂, while the transmitted field is Eₜ = E₀ₜ e^{i(k₂z −

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