  We study the propagation of light in the Born-Infeld (BI) background as seen
by an accelerated observer. In a Born-Infeld electromagnetic field, light
trajectories are governed by the null geodesics of the effective optical
metric. The accelerated observer is in a Rindler frame, a situation that,
according to the Einstein Equivalence Principle, is equivalent to being in a
uniform gravitational field. The phase velocity of light propagating through a
purely magnetic or electric BI background is determined as measured by the
Rindler observer. The BI field and the acceleration of the frame have opposite
effects on the propagating light: while the intense electric or magnetic BI
background slows down the velocity of light, in the accelerated frame light may
exceed its velocity in vacuum. We consider light propagating parallel or
transversal to the acceleration direction of the Rindler frame. The redshift of
light pulses sent from one Rindler observer to another, in the BI background,
is calculated as well.
