Converging Thick Lens with Principal Planes: A Geometric Imaging Demonstration

This example demonstrates how a converging thick lens forms an image by constructing an equivalent geometric ray diagram around the principal planes. By building rays, reference lines, and intersection points, it visualizes how incident rays are redirected to meet at an image point, clarifying the relationship between object distance, image distance, and the lens’s principal planes. Key mathematical concepts include geometric construction with points, rays, lines, segments, and angle measurement, where angles (e.g., α, β, γ) constrain the ray configuration; geometric intersection is used to locate the image. The construction leverages GeoGebra commands and objects extracted from the provided summary: Point to define key points (lens-related, object/image points, principal-plane markers), Line/Segment for ray paths and geometric scaffolding, Ray for directed incident rays, CircleArc and Circle for auxiliary curved/curvature-like references, Angle for marking critical angles, Intersect to compute the convergence/image location, and transformations such as Mirror and Rotate for equivalent optical-path construction. Text objects (text1, text2) are used for clear labeling. Suitable for high-school to early university physics/math lessons on geometric optics and for learners using GeoGebra to connect algebraic/functional ideas with visual geometric imaging relationships.