Using a linear approximation for single-surface refraction to explain some virtual image phenomena

Abstract

There are many examples of interesting optical phenomena involving virtual images arising from refraction at the interface(s) between air and some transparent solid or liquid. However, because it is cumbersome to interpret analytical expressions or to sketch diagrams using Snell’s law of refraction, students rarely explore and develop a qualitative understanding of these phenomena. In this paper we introduce a simple-to-use linear approximation for single-surface refraction and show how it leads to qualitatively correct descriptions of some interesting but complex optical phenomena. In particular, we analyze the virtual images formed when looking at objects through both rectangular blocks and triangular prisms. The refraction images observed through a triangular prism are particularly interesting pedagogically and also provide a physical means to distinguish between objects located just outside and just inside, or on, the prism’s surface.