Fluids of mesoscopic thickness can be sheared and their molecular orientation probed concurrently with the new instrument described in this paper. The fluid is confined between parallel optically flat windows whose spacing is controlled, using piezoelectric inchworms, from submicrometer thickness to similar to 500 mu m, with no essential lower limit apart from surface roughness. Capacitance sensors or optical interferometry is used to monitor spacing between the windows with submicrometer accuracy. Piezoelectric bimorphs are used to apply periodic shear displacements with amplitude 0.1-10 mu m and frequency 0.1-700 Hz. Shear-induced molecular alignment during sinusoidal shear cycles is determined, with up to 5 mu s time resolution, using step-scan time-resolved infrared spectroscopy. To demonstrate capabilities of this new instrument, we describe an experiment in which shear and electric fields were applied in orthogonal directions to 5-cyanobiphenyl (5CB), a simple nematic Liquid crystal. Provided that the molecule lacked the time to relax during the period of oscillation, the molecule tilted back and forth around the equilibrium orientation under the action of small-amplitude oscillating shear. The shear alignment appeared to be proportional to the shear displacement, not to the effective shear rate.