Multi-Band Optical Variability Characteristics of the $γ$-ray emitting blazar 1ES 0647+250 during its 2020 flare
We present a multi-band optical variability study of the $γ$-ray emitting high-synchrotron-peaked blazar 1ES~0647+250 during its enhanced optical activity in 2020. The analysis utilizes 107 epochs of high-precision $B$, $V$, and $R$-band photometry obtained with the 75 cm telescope at the Vainu Bappu Observatory, combined with high-cadence $z_g$ and $z_r$ survey data from the Zwicky Transient Facility. The combined light curves reveal coherent variability across all optical filters, with the source reaching a peak $R$-band magnitude of 15.74 mag. We calculated the variability amplitude, finding the highest intrinsic variability in the B- band. Spectral analysis using color--magnitude diagrams reveals a statistically significant ``Bluer-When-Brighter'' trend, supported by a Pearson correlation coefficient of $r = 0.68$ ($p < 0.001$) for the (V$-$R) index. Furthermore, the discrete correlation function analysis indicates a near-zero time lag between the $V$ and $R$ bands, suggesting simultaneous emission within the observational cadence. The observed spectral hardening is consistent with synchrotron-dominated optical emission, likely associated with enhanced particle acceleration within the jet during the active phase of 1ES~0647+250.