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A stack of transparent plates with randomly varying thicknesses (e.g. viewgraphs) reflects light perfectly, as a result of the accumulation of reflections from interfaces at the air gaps separating the plates. Two theories of this effect are discordant. The naive ray theory assumes that the random phases associated with the thickness variations make all the reflections incoherent, and predicts that the transmitted intensity decays as 1/N. This theory is wrong because some distinct multiply reflected waves have identical path lengths and so superpose coherently. The true decay is exponential: exact averaging of the logarithm of the transmitted intensity over the random phases, assuming these are uniformly distributed modulo , gives the transmitted intensity as , where is the intensity transmittance of a single interface. Transparent mirrors are naked-eye examples of the localization of light, for which the localization length (inverse decay exponent) can be calculated exactly. Experiments confirm the exponential decay.
Berry et al. (Thu,) studied this question.
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