Einstein Ring — Gravitational Lensing

When a massive object lies between observer and source, light bends around it. Perfect alignment produces an Einstein ring. The deflection angle α = 4GM/c²b (Schwarzschild), double the Newtonian prediction — confirmed by Eddington in 1919.

Lens Parameters

Lens mass M (Einstein radii) 1.00

Source offset β 0.00

Source size 0.15

Ray density 200

Einstein radius θ_E1.00

Magnification μ—

Images—

Source offset β0.00

α = 4GM/c²b (deflection)

Lens equation:
β = θ - θ_E²/θ

Solutions: θ± = (β ± √(β²+4θ_E²))/2

Magnification:
μ = |u⁴/(u⁴-1)| where u=β/θ_E

β=0: Einstein ring θ=θ_E