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 850micron.
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