We analyze the infrared reflectivity of Lal.85Sr0.~sCuO4 single crystals with E parallel to the c-axis. The plasma edge at around 6 meV (50 cm-I), which occurs only for T < T¢, is due to Cooper-pair tunneling. This low value of the plasma edge is shown to be consistent with the c-axis plasma frequency obtained from LDA band structure calculations (> 0.1 eV) if we take into account that the single-particle charge transport along the c-axis is strongly incoherent in the normal state, and remains so in the superconducting state. From a comparison of the optical conductivity with model calculations based on sand d-wave weak-coupling theory in the dirty limit, we find no evidence for a reduction of the c-axis quasi-particle scattering rate below T~. The c-axis scattering rate, the normal-state c-axis plasma frequency, and Tc obey hT > hvp >> 3.5kBTc, which is exactly opposite to the clean limit.
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