We have studied the opacity of dust grains at submillimeter wavelengths by estimating the optical depth from imaging at 160, 250, 350, and 500 um from the Herschel Gould Belt Survey and comparing this to a column density obtained from the 2MASS-derived color excess E(J-Ks). Our main goal was to investigate the spatial variations of the opacity due to "big" grains over a variety of environmental conditions and thereby quantify how emission properties of the dust change with column (and volume) density. The central and southern areas of the Orion A molecular cloud examined here, with NH ranging from 1.5X10^21 cm^-2 to 50X10^21 cm^-2, are well suited to this approach. We fit the multi-frequency Herschel spectral energy distributions (SEDs) of each pixel with a modified blackbody to obtain the temperature, T, and optical depth, \tau(1200), at a fiducial frequency of 1200 GHz (250 um). Using a calibration of NH/E(J-Ks)for the interstellar medium (ISM) we obtained the opacity (dust emission cross-section per H nucleon), \sigma_e(1200), for every pixel. From a value of ~ 1X10^-25 cm^2 H^-1 at the lowest column densities that is typical of the high latitude diffuse ISM, \sigma_e(1200) increases as NH^0.28 over the range studied. This is suggestive of grain evolution. Integrating the SEDs over frequency, we also calculated the specific power P (emission power per H) for the big grains. In low column density regions where dust clouds are optically thin to the interstellar radiation field (ISRF), P is typically 3.7 X 10^-31 W H^-1, again close to that in the high latitude diffuse ISM. However, we find evidence for a decrease of P in high column density regions, which would be a natural outcome of attenuation of the ISRF that heats the grains, and for localized increases for dust illuminated by nearby stars or embedded protostars.