Gravitational Lensing — Einstein Ring
Light deflection by massive objects: α = 4GM/c²b (general relativity)
Lens Parameters
Lens mass (M/M☉ ×10⁸):
5
Source offset (arcsec):
0.0
Source distance (Gpc):
2.0
Lens distance (Gpc):
1.0
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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.