A flexible sheet-form optical system, referenced to as a light redirecting fabric, which has a fabric-like behavior and light redirecting properties. The light redirecting fabric comprises a soft and flexible sheet of optically transmissive material, such as plasticized polyvinyl chloride. A surface of the flexible sheet includes a plurality of parallel slits having spaced-apart walls configured to reflect light by means of a total internal reflection. At least a portion of daylight incident onto the sheet is internally redirected at bend angles greater than the angle of incidence. Disclosed also are a method and apparatus for making the light redirecting fabric. The method includes steps of mechanical slitting of the flexible sheet with a blade, elastic stretch-elongation of the sheet along a direction perpendicular to the slits, and making at least a portion of the sheet elongation irreversible.