We present three methods for measuring the slope of the Galactic dust extinction law , R _ { V } , and a method for measuring the fine-scale structure of dust clouds in the direction of differentially-reddened globular clusters .
We apply these techniques to BVI photometry of stars in the low-latitude Galactic globular cluster NGC 4833 which displays spatially-variable extinction/reddening about a mean \langle { A _ { V } } \rangle \approx 1 .
An extensive suite of Monte Carlo simulations is used to characterize the efficacy of the methods .
The essence of the first two methods is to determine , for an assumed value of R _ { V } , the relative visual extinction \delta { A _ { V } } of each cluster horizontal branch ( HB ) star with respect to an empirical HB locus ; the locus is derived from the color-magnitude diagram ( CMD ) of a subset of stars in a small region near the cluster center for which differential extinction/reddening are relatively small .
A star-by-star comparison of \delta { A _ { V } } from the ( B - V , V ) CMD with that from the ( V - I , V ) CMD is used to find the optimal R _ { V } .
In the third method , R _ { V } is determined by minimizing the scatter in the HB in the ( B - V , V ) CMD after correcting the photometry for extinction and reddening using the Schlegel , Finkbeiner , & Davis ( 1998 ) dust maps .
The weighted average of the results from the three methods gives R _ { V } = 3.0 \pm 0.4 
for the dust along the line of sight to NGC 4833 .
The fine-scale structure of the dust is quantified via the difference , ( \Delta { A _ { V } } ) _ { ij } \equiv ( \delta { A _ { V } } ) _ { i } - ( \delta { A _ { V } } ) _ { j } , between pairs of cluster HB stars ( i , j ) as a function of their angular separation r _ { ij } .
The variance ( mean square scatter ) of ( \Delta { A _ { V } } ) _ { ij } is found to have a power-law dependence on angular scale : { var } ( r ) \propto { r } ^ { \beta } , with \beta = +0.9 \pm 0.1 .
This translates into an angular power spectrum P ( \kappa ) \propto \kappa ^ { \alpha } , with the index \alpha = -1.9 \pm 0.1 for r \sim 1 ^ { \prime } – 5 ^ { \prime } , where \kappa \equiv 1 / r .
The dust angular power spectrum on small scales ( from optical data ) matches smoothly onto the larger-scale power spectrum derived from Schlegel et al. ’ s far-infrared map of the dust thermal emission .