Using a smartphone camera to explore ray optics beyond the thin lens equation

Abstract

Ray optics is a staple of introductory physics classes, but many students do not have the opportunity to explore optics beyond the thin lens equation. In this paper, we expand upon a successful remote experiment using a smartphone camera to explore both the successes and limitations of the thin lens equation. Application of the thin lens equation reveals a linear relationship between the object distance and the inverse image height in pixels. Using the open-source image analysis tool ImageJ to measure the image height, we can find the effective focal length of the smartphone camera lens. Our measured focal lengths agree well with the stated manufacturer values for the effective focal lengths. Further application of the thin lens equation is not successful, but a modification of the analysis leads to an explanation and experimental determination of the location of the principal planes in the smartphone camera systems. This experiment can work well at the introductory level, either in person or remote, and can be used as an introduction or motivation to explore more advanced topics in ray optics.