A circumzenithal arc to study optics concepts with geometrical optics

Abstract

This paper describes the formation of a circumzenithal arc for the purpose of teaching light and optics. A circumzenithal arc, an optic formation rarely witnessed by people, is formed in this study using a water-filled cylindrical glass illuminated by sunlight. Sunlight refracted at the top and side surfaces of the glass of water is dispersed into its constituent colours. First, multi-colour arcs are observed on paper at the bottom of the glass. Then, a single arc for each colour is observed on the floor when the rays are allowed to propagate to the furthest points from the glass. The change in observations is explained by formulating an equation for the geometry of the situation. The formula relates each point on the first refracting surface for an incoming light ray to a point further from the second refracting surface. Then, a parallel graph is drawn to visualize the superposition of colours to the formation of a single arc. The geometrical optics studies in this paper exemplify the concept of Snell's law, total internal reflection and dispersion. The duration of the observation on a circumzenithal arc is limited by the altitude of the Sun in the sky. This study depends on the use of astronomy software to track solar altitude. Pedagogical aspects of the study are discussed for inquiry-based teaching and learning of light and optics concepts. © 2017 IOP Publishing Ltd.