  We show that very-long-baseline-interferometry (VLBI) observations of
supermassive black holes will allow us to test the fundamental principles of
General Relativity (GR). GR is based on the universality of gravity and
Einstein's equivalence principle (EEP). However, EEP is not a basic principle
of physics but an empirical fact. Non-minimal coupling (NMC) of electromagnetic
fields violates EEP, and their effects manifest in the strong-gravity regime.
Hence, VLBI observations of black holes provide an opportunity to test NMC in
the strong-gravity regime. To the leading order in the spin parameter, we
explicitly show that the NMC of the electromagnetic field introduces observable
modifications to the black hole image. In addition, we find that the size of
the photon rings varies by $\sim 3 r_H$, which corresponds to $\sim 30 \mu as$
for Sagittarius $A^*$ and $\sim 23 \mu as$ for M87. VLBI telescopes are
expected to attain a resolution of $\sim 5 \mu as$ in the near future. However,
direct detection of photon ring will require the resolution of $\sim 1 \mu as$
for M87, which can potentially be probed by the space-based Event Horizon
Explorer.
