We present observations and modeling of a lunar occultation of the dust-enshrouded carbon star AFGL 5440. The observations were made over a continuous range of wavelengths from 1 - 4um with a high-speed spectrophotometer designed expressly for this purpose. We find that the occultation fringes cannot be fit by any single-size model. We use the DUSTY radiative transfer code to model a circumstellar shell and fit both the observed occultation light curves and the spectral energy distribution described in the literature. We find a strong constraint on the inner radius of the dust shell, Tmax = 950 K +/- 50K, and optical depth at 5um of 0.5 +/- 0.1. The observations are best fit by models with a density gradient of r^-2 or the gradient derived by Ivezic & Elitzur for a radiatively driven hydrodynamic outflow. Our models cannot fit the observed IRAS 60um flux without assuming a substantial abundance of graphite or by assuming a substantially higher mass-loss rate in the past.
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