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 – 4µm with a high-speed spectrophotometer designed expressly for this purpose .
We find that the occultation fringes can not 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 , T _ { max } = 950 K \pm 50K , and optical depth at 5µm of 0.5 \pm 0.1 .
The observations are best fit by models with a density gradient of \rho \propto r ^ { -2 } or the gradient derived by Ivezić & Elitzur for a radiatively driven hydrodynamic outflow .
Our models can not fit the observed IRAS 60µm flux without assuming a substantial abundance of graphite or by assuming a substantially higher mass-loss rate in the past .