Geometric Optics

Diverging (Concave) Lens Ray Diagram Simulator (Myopia Optics)

Verify why a concave lens (f < 0) always forms an upright, diminished virtual image inside the near focal length regardless of object distance.

Real-Time RK4 Kinematic / Dynamical Waveform Recorder

Physical Principles & Mathematical Derivation

f < 0 ⇒ dᵢ = −(|f| × dₒ) / (dₒ + |f|), 0 < M < 1

Biconcave lenses possess negative optical power (diopters < 0), spreading incident rays outward as if originating from the near-side focal point F. Used in eyeglasses to correct nearsightedness (myopia), they always produce 0 < M < 1 upright virtual images.

Questions & Concepts

What physical equation governs Diverging (Concave) Lens Ray Diagram Simulator (Myopia Optics)?

f < 0 ⇒ dᵢ = −(|f| × dₒ) / (dₒ + |f|), 0 < M < 1 — Biconcave lenses possess negative optical power (diopters < 0), spreading incident rays outward as if originating from the near-side focal point F. Used in eyeglasses to correct nearsightedness (myopia), they always produce 0 < M < 1 upright virtual images.

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.

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