  Infrared extinction maps and submillimeter dust continuum maps are powerful
probes of the density structure in the envelope of star-forming cores. We make
a direct comparison between infrared and submillimeter dust continuum
observations of the low-mass Class 0 core, B335, to constrain the ratio of
submillimeter to infrared opacity (\kaprat) and the submillimeter opacity
power-law index ($\kappa \propto \lambda^{-\beta}$). Using the average value of
theoretical dust opacity models at 2.2 \micron, we constrain the dust opacity
at 850 and 450 \micron . Using new dust continuum models based upon the broken
power-law density structure derived from interferometric observations of B335
and the infall model derived from molecular line observations of B335, we find
that the opacity ratios are $\frac{\kappa_{850}}{\kappa_{2.2}} = (3.21 -
4.80)^{+0.44}_{-0.30} \times 10^{-4}$ and $\frac{\kappa_{450}}{\kappa_{2.2}} =
(12.8 - 24.8)^{+2.4}_{-1.3} \times 10^{-4}$ with a submillimeter opacity
power-law index of $\beta_{smm} = (2.18 - 2.58)^{+0.30}_{-0.30}$. The range of
quoted values are determined from the uncertainty in the physical model for
B335. For an average 2.2 \micron\ opacity of $3800 \pm 700$ cm$^2$g$^{-1}$, we
find a dust opacity at 850 and 450 \micron\ of $\kappa_{850} = (1.18 -
1.77)^{+0.36}_{-0.24}$ and $\kappa_{450} = (4.72 - 9.13)^{+1.9}_{-0.98}$
cm$^2$g$^{-1}$ of dust. These opacities are from $(0.65 - 0.97)
\kappa^{\rm{OH}5}_{850}$ of the widely used theoretical opacities of Ossenkopf
and Henning for coagulated ice grains with thin mantles at 850\micron.
