This application describes a back-lit transmissive display including a transmissive display and a variable index light extraction layer optically coupled to a lightguide. The variable index light extraction layer has first regions of nanovoided polymeric material and second regions of the nanovoided polymeric material and an additional material. The first and second regions are disposed such that for light being transported at a supercritical angle in the lightguide, the variable index light extraction layer selectively extracts the light in a predetermined way based on the geometric arrangement of the first and second regions. The transmissive display may be a transmissive display panel or a polymeric film such as a graphic.