Gravitational Lensing — Einstein Ring

Light deflection by massive objects: α = 4GM/c²b (general relativity)

Lens Parameters

Einstein radius θ_E:
Ring/arc type:
Magnification:
Einstein ring: source exactly behind lens → perfect ring with radius θ_E = √(4GM D_ls / c² D_l D_s)

Off-axis: two arcs (major/minor images). Convergence κ = Σ/Σ_cr. Point mass lens map: β = θ − θ_E²/θ

Strong lensing by galaxy clusters reveals dark matter distribution.