Assessing the Refractive Index of Glass Beads for Use in Road-marking Applications via Retroreflectance Measurement

Abstract

Retroreflection of vehicle headlights, as induced by spherical glass beads, is a key optical phenomenon that provides road-surface markings with greatly enhanced visibility, thus better securing a driver’s safety in the nighttime as well as in unclear daytime. Retroreflectance of glass beads is a quite sensitive function of their refractive index, so that measurement of the refractive index of glass specifically in the shape of spherical beads needs to be performed within a reasonable uncertainty that is tolerable for road-marking applications. The Becke line method has been applied in assessing refractive index of such glass beads as e.g. an industrial standard in the Republic of Korea; however, the reference refractive-index liquids are not commercially available these days for refractive index greater than 1.80 due to the toxicity of the constituent materials. As such, high-refractive-index glass beads require an alternate method, and in this regard we propose a practically serviceable technique with uncertainty tantamount to that of the Becke line method: Based on comparison of calculated and measured retroreflectance values of commercial glass beads, we discover that their refractive index can be determined with reasonable precision via the retroreflectance measurement. Specifically, in this study the normalized retroreflectance originating from a single glass sphere is computed as a function of refractive index using the Fresnel equations, which is then validated as coinciding well with retroreflectance values measured from actual specimens, i.e. glass-bead aggregates. The uncertainties involved are delineated in connection with radius and imperfections of the glass beads.