Determining the Focal Length of Converging and Diverging Lenses Using a Smartphone

In this study, we propose a novel and direct method of determining the focal length of a converging or diverging lens using a smartphone. The standard optical sensor used in modern smartphone cameras is an active-pixel sensor called the complementary metal–oxide–semiconductor (CMOS). The CMOS is covered by an assembly of five to seven camera lenses that can be moved along the axis of the camera to electronically adjust its overall effective focal length, i.e., the autofocus feature. This collection of lenses, referred to as a system of adaptive optical lenses, can be treated as a single effective converging lens that forms a real image on the CMOS sensor array. We assume that the image distance between the CMOS sensor array and the smartphone camera lens (SCL) is a constant. Based on this assumption, a two-step procedure is proposed to accurately obtain the focal length of a lens without the need for additional lenses.