Gravitational Lensing & Light Deflection

General relativity bends light — Einstein rings, arcs & multiple images

Parameters

General Relativistic Lensing

Deflection angle: α = 4GM/(c²b) where b is impact parameter. Factor 4 vs Newtonian (factor 2) — GR prediction confirmed by Eddington 1919.

Lens equation: β = θ − (θE/θ)² where θE = √(4GM·Dls/(c²·Ds·Dl)) is the Einstein radius.

Einstein ring: Source exactly behind lens → perfect ring of angular radius θE.

Multiple images: Off-axis source → two images (+ + −) with magnification |μ| = |u²+2|/(|u|√(u²+4)) where u = β/θE.