  Despite possessing a local spin $2$ moment on the iron site and a Curie-Weiss
temperature of $45K$, the A site spinel FeSc$_2$S$_4$ does not magnetically
order down to 50mK. Previous theoretical work by Chen and Balents advanced an
explanation for this observation in the form of the "$J_2$-$\lambda$" model
which places FeSc$_2$S$_4$ close to a quantum critical point on the disordered
side of a quantum phase transition between a N\'{e}el ordered phase and a
"Spin-Orbital Liquid" in which spins and orbitals are entangled, quenching the
magnetization. We present new theoretical studies of the optical properties of
the $J_2$-$\lambda$ model, including a computation of the dispersion relation
for the quasiparticle excitations and the form of the collective response to
electric field. We argue that the latter directly probes a low energy
excitation continuum characteristic of quantum criticality, and that our
results reinforce the consistency of this model with experiment.
