  The ratio between the Land\'e g-factors of the $^{87}$Rb $F=2$ and $^{85}$Rb
$F=3$ ground state hyperfine levels is experimentally measured to be
$g_F(87)/g_F(85) = 1.4988586(1)$, consistent with previous measurements. The
g-factor ratio is determined by comparing the Larmor frequencies of overlapping
ensembles of $^{87}$Rb and $^{85}$Rb atoms contained within an evacuated,
antirelaxation-coated vapor cell. The atomic spins are polarized via
synchronous optical pumping and the Larmor frequencies are measured by
off-resonant probing using optical rotation of linearly polarized light. The
accuracy of this measurement of $g_F(87)/g_F(85)$ exceeds that of previous
measurements by a factor of $\approx 50$ and is sensitive to effects related to
quantum electrodynamics.
