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Statement of a problem № 3958

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An electromagnetic wave, propagating and linearly polarized in the xz-plane, is incident onto an interface between two non-conducting media as shown in Fig. 14.10. The electric fields and propagation vectors of the incident, reflected and transmitted waves are denoted by EI, ER, ET, kI, kR and kT respectively. The wave is incident onto the interface at the origin and makes an angle T to the normal. Both incident and reflected waves propagate in the medium with refractive index n1 . The transmitted wave propagates in the medium with refractive index n2 at refraction angle I†. Use the boundary conditions satisfied by the electric field at the interface to show that the reflectance, R, is given by R=((n2cosT-n1cosf)/(n2cosT+n1cosf))^2

Solution:
An electromagnetic wave, propagating and linearly polarized in the xz-plane, is

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