Consider a dielectric layer of permittivity_2 separating two dielectric media of

Question

Consider a dielectric layer of permittivity_2 separating two dielectric media of permittivity_1 _2, with the interfaces located at z = 0 and z = d. What are the boundary conditions at these two interaces? (These are the 4 equations you would solve in order to calculate the transmission and reflection of a plane wave from this layer.) Where does the thickness d appear in these equations? Determine how the reflectivity varies with the thickness. (Since there are 4 equations in 4 unknowns, it is easier to solve the system of equations numerically, but an analytical solution is possible and acceptable.)

Explanation / Answer

Here, Boundary condition at z = 0

=> (E1 - E2)/E3   > d

Here, Boundary condition at z = d

=>   (E3 - E2)/E1 > (d - 1)

Here, reflectivity is directly proportional to   (1/E) .

=>    reflectivity is inversely proportional to   d .

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