Non-contact tonometry (NCT) is a non-invasive ophthalmologic technique to measure intraocular pressure (IOP) using an air puff for routine glaucoma testing. Although IOP measurement using NCT has been perfected over many years, various phenomenological aspects of interfacial physics, fluid structure interaction, waves on corneal surface, and pathogen transmission routes to name a few are inherently unexplored. Research investigating the interdisciplinary physics of the ocular biointerface and of the NCT procedure is sparse and hence remains to be explored in sufficient depth. In this perspective piece, we introduce NCT and propose future research prospects that can be undertaken for a better understanding of the various hydrodynamic processes that occur during NCT from a pathogen transmission viewpoint. In particular, the research directions include the characterization and measurement of the incoming air puff, understanding the complex fluid-solid interactions occurring between the air puff and the human eye for measuring IOP, investigating the various waves that form and travel; tear film breakup and subsequent droplet formation mechanisms at various spatiotemporal length scales. Further, from an ocular disease transmission perspective, the disintegration of the tear film into droplets and aerosols poses a potential pathogen transmission route during NCT for pathogens residing in nasolacrimal and nasopharynx pathways. Adequate precautions by opthalmologist and medical practioners are therefore necessary to conduct the IOP measurements in a clinically safer way to prevent the risk associated with pathogen transmission from ocular diseases like conjunctivitis, keratitis, and COVID-19 during the NCT procedure.