Beam Asymmetry in $\gamma$p $\rightarrow$ $\eta$ $\Delta^+$ at GlueX

The photo-production mechanism used in the \textsc{GlueX} experiment by impinging an 8.2-8.8 GeV linearly polarized photon beam on a liquid hydrogen target allows the mapping of light mesons in unprecedented detail with particular interest in exotic meson candidates. Polarization observables such as beam asymmetry $\Sigma$, extracted from azimuthal ($\phi$) angular distributions between the meson production plane and the polarized photon beam, help in understanding production mechanisms and quasi-particle exchange processes using Regge theory. We report preliminary results on the beam asymmetry measurements for $\eta$ in $\gamma$p $\rightarrow$ $\eta$ $\Delta^+$. The reaction $\gamma$p $\rightarrow$ $\eta$ $\Delta^+$ provides an opportunity for validation of previous $\eta$ asymmetry measurements and theoretical calculations.