Gravitational Lensing Calculator

Mass bends spacetime, deflecting light passing nearby. In LFM, photons follow null geodesics through the χ field — curved paths emerge from the lattice structure.

⭐ Historic Confirmation: 1919 Eclipse

Eddington's expedition measured starlight deflection during a total solar eclipse. Result: 1.75" ± 0.16"

This was 2× the Newtonian prediction (0.87"), confirming Einstein's General Relativity and making headlines worldwide.

Newtonian (1801): θ = 2GM/bc²
→ 0.875" at solar limb
Einstein GR (1915): θ = 4GM/bc²
→ 1.75" at solar limb ✓

LFM Mechanism

In LFM, light deflection arises from the χ field gradient. Near a mass, χ < χ₀, creating an effective refractive index n_eff = χ₀/χ. Light slows down (in coordinate time) where χ is depressed, causing the wavefront to bend toward the mass.

Deflection angle: θ = 4GM/bc² = 2 × ∫ (∇n_eff/n_eff) dl

Select Lens

Results

Deflection Angle (GR)
θ = 1.751"
= 1.7510" = 8.489 μrad
Newtonian (1801)
0.875"
= 2GM/bc²
GR / LFM (1915)
1.751"
= 2× Newtonian ✓
Einstein Ring Radius
Angular
40.991"
Physical (at lens)
29.73 Mm
Perfect alignment produces a ring of this angular radius
Schwarzschild Radius2.95 km
Impact / r_s2.36e+5
χ/χ₀ at Impact0.9999978778
Magnification (tangential)×1.342

Light Deflection Visualization

Source
Lens
Observer

Light bends toward the mass. For strong lensing (galaxies, clusters), multiple images or arcs are visible.

Gravitational lensing predicted by Einstein (1915), confirmed by Eddington (1919).
LFM derives the same 4GM/bc² from χ field refraction (GOV-01 + GOV-02).