In the late 18th century, a chemist somewhere in the West discovers a cheap and easy process that can be used to produce glass with a negative refractive index. What use would society have for this invention, if any?
Better, cheaper, lighter lenses. Better refractive telescopes and better microscopes. And, eventually, better photolithography.
Negative-index converging lenses are concave rather than convex. That means the center is thinner, resulting in better clarity. Additionally, negative-index lenses can amplify near-field electromagnetic effects, allowing them to defeat the diffraction limit on resolution, which means you can use lenses with smaller diameters for equal resolutions. You could also pair negative-index and positive-index components to create flat lenses, which would be easier to build mounts for and integrate into other structures. And, if you can match dispersion profiles, negative-index glass paired with positive-index glass would make it easier to build lenses with minimal chromatic aberration.