Reflection and Transmission at a Plane Boundary

The considerations in the preceding section make it worthwhile to discuss reflection and transmission at plane boundaries first, one plane boundary separating infinite media, then in the next section two successive plane boundaries forming a slab. In addition to providing useful results for bulk materials, these relatively simple boundary-value problems illustrate methods used in more complicated small-particle problems. Also, the optical properties of slabs often will be compared to those of small particles—both similarities and differences—to develop intuitive thinking about particles by way of the more familiar properties of bulk matter. 

Consider a plane wave propagating in a nonabsorbing medium with refractive index N2 = n2, which is incident on a medium with refractive index A, = w, + iky (Fig. 2.4). The amplitude of the incident electric field is E(, and we assume that there are transmitted and reflected waves with amplitudes E, and Er, respectively. Therefore, plane-wave solutions to the Maxwell equations at 

The tangential components of the electric field are required to be continuous across the boundary z — 0  

Continuity of the tangential magnetic field yields the condition 

Note that R X 100% is close to 100% if either n 1 or n 1 or k 1. One might think that a material with k 1 would be highly absorbing. But such a material is highly reflecting, and an incident wave cannot get into the material to be absorbed. 

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