IGNOU BPHCT 137 2026 - Obtain expressions for reflection and transmission amplitude coefficie

Question

Obtain expressions for reflection and transmission amplitude coefficients when electric vector associated with a plane monochromatic electromagnetic wave is in the plane of incidence.

19 Jan 2026

Answer :

Word Count : 529

When a plane monochromatic electromagnetic wave is incident on the boundary separating two dielectric media, the interaction of the wave with the interface results in partial reflection and transmission. The plane of incidence is defined by the incident wave vector and the normal to the surface. If the electric vector of the wave lies in the plane of incidence, the polarization is called p-polarized (or parallel polarization). To derive the reflection and transmission amplitude coefficients for p-polarized light, we start with Maxwell's equations and boundary conditions. Let the incident wave propagate from medium 1 with refractive index ( n_1 ) to medium 2 with refractive index ( n_2 ). The electric field of the incident wave can be expressed as: [ \mathbf{E}_i = E_i , \hat{p} , e^{i(\mathbf{k}_1 \cdot \mathbf{r} - \omega t)} ] where ( \hat{p} ) is the unit vector in the direction of the electric field lying in the plane of incidence, ( \mathbf{k}_1 ) is the wave vector in medium 1, and ( \omega ) is the angular frequency. Similarly, the reflected and transmitted electric fields are: [ \mathbf{E}_r = E_r , \hat{p}_r , e^{i(\mathbf{k}_r \cdot

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