Physical Principles & Mathematical Derivation
A biconvex converging lens refracts parallel paraxial rays through its real focal point F′. When the object sits beyond 2F, a reduced, real, inverted image forms (camera sensor); between 2F and F, an enlarged real image forms (cinema projector); inside F, rays diverge to create an upright virtual image!
Questions & Concepts
What physical equation governs Converging (Convex) Lens Ray Diagram & Image Simulator?
1 / f = 1 / dₒ + 1 / dᵢ, M = −dᵢ / dₒ = hᵢ / hₒ — A biconvex converging lens refracts parallel paraxial rays through its real focal point F′. When the object sits beyond 2F, a reduced, real, inverted image forms (camera sensor); between 2F and F, an enlarged real image forms (cinema projector); inside F, rays diverge to create an upright virtual image!
How are the equations of motion integrated in this simulation?
Nonlinear differential equations are integrated at 240–300 Hz substeps using classical 4th-order Runge-Kutta (RK4) to maintain strict Hamiltonian energy accuracy.