High entropy oxides (HEOs) are single phase solid solutions consisting of 5 or more cations in approximately equiatomic proportions. In this study, we show reversible control of optical properties in a rare-earth (RE) based HEO-(Ce$_{0.2}$La$_{0.2}$Pr$_{0.2}$Sm$_{0.2}$Y$_{0.2}$)O$_{2-delta}$ and subsequently utilize a combination of spectroscopic techniques to derive the features of the electronic band structure underpinning the observed optical phenomena. Heat treatment of the HEO under vacuum atmosphere followed by reheat-treatment in air results in a reversible change of the band gap energy, from 1.9 eV to 2.5 eV. The finding is consistent with the reversible changes in the oxidation state and related $f$-orbital occupancy of Pr. However, no pertinent changes in the phase composition or crystal structure is observed upon the vacuum heat treatment. Further annealing of this HEO under H$_2$ atmosphere, followed by reheat-treatment in air, results in even larger but still reversible change of the band gap energy from 1.9 eV to 3.2 eV. This is accompanied by a disorder-order type crystal structure transition and changes in the O 2$p$-RE 5$d$ hybridization evidenced from X-ray absorption near edge spectra (XANES). The O $K$ and RE ${M_{4,5}}$/$L_{3}$ XANES indicate that the presence of Ce and Pr (in 3+/4+) state leads to the formation of intermediate 4$f$ energy levels between the O 2$p$ and RE 5$d$ gap in HEO. It is concluded that heat treatment under reducing/oxidizing atmospheres affects these intermediate levels, thus, offering the possibility to tune the band gap energy in HEO.
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