Wormhole Throat Geodesics: Photon Transmission vs. Reflection (2D)

The 3D Wormhole Portal is a shader-driven flythrough: it looks like a traversable wormhole but doesn't compute one. This 2D companion does the actual physics. It builds the embedding profile of a Morris–Thorne wormhole with the simplest shape function, r(l) = √(l² + r₀²), where l is proper distance along the throat's axis and r₀ is the throat radius, and draws it as a funnel cross-section connecting two universes. A stream of photons is then fired along that axis, each with its own impact parameter b, and every photon's radial motion is integrated from the real null-geodesic equation (dl/dλ)² = 1 − b²/r(l)². Because r(l) never drops below r₀, a photon with b ≤ r₀ always has a positive right-hand side and sails straight through the throat into the far universe; a photon with b > r₀ hits a genuine turning point where r(l) = b, the same way a particle reflects off a classical potential barrier, and is sent back the way it came. A live effective-potential chart plots b²/r(l)² against the horizontal line at 1 so the turning point is visible as the exact crossing, and a highlighted photon accumulates its true bending angle Δφ = ∫ (b/r(l)²) dλ as it travels, letting you watch gravitational lensing add up in real time rather than just look decorative.