The alignment of interstellar dust grains with magnetic fields provides a key method for measuring the strength and morphology of the fields. In turn, this provides a means to study the role of magnetic fields from diffuse gas to dense star-forming regions. The physical mechanism for aligning the grains has been a long-term subject of study and debate. The theory of radiative torques, in which an anisotropic radiation field imparts sufficient torques to align the grains while simultaneously spinning them to high rotational velocities, has passed a number of observational tests. Here we use archival polarization data in dense regions of the Orion molecular cloud (OMC-1) at 100, 350, and $850,mu$m to test the prediction that the alignment efficiency is dependent upon the relative orientations of the magnetic field and radiation anisotropy. We find that the expected polarization signal, with a 180-degree period, exists at all wavelengths out to radii of 1.5 arcminutes centered on the BNKL object in OMC-1. The probabilities that these signals would occur due to random noise are low ($lesssim$1%), and are lowest towards BNKL compared to the rest of the cloud. Additionally, the relative magnetic field to radiation anisotropy directions accord with theoretical predictions in that they agree to better than 15 degrees at $100,mu$m and 4 degrees at $350,mu$m.
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