  We measure the optical absorption spectra and optical conductivities of
excitons and trions in monolayers of metal dichalcogenide MoS$_{2}$ and compare
the results with theoretical models. Our results show that the Wannier-Mott
model for excitons, with modifications to account for small exciton radii and
large exciton relative wavefunction spread in momentum space, phase space
blocking due to Pauli exclusion in doped materials, and wavevector dependent
dielectric constant, gives results that agree well with experiments. The
measured exciton optical absorption spectra are used to obtain experimental
estimates for the exciton radii that fall in the $7-10\AA$ range and agree well
with theory. The measured trion optical absorption spectra are used to obtain
values for the trion radii that also agree well with theory. The measured
values of the exciton and trion radii correspond to binding energies that are
in good agreement with values obtained from first principles calculations.
