🌌 Gravitational Lensing — Einstein Ring
Massive objects curve spacetime, bending light paths around them. When a background source, massive lens, and observer are perfectly aligned, light travels around all sides of the lens forming a complete Einstein ring. For off-axis sources, multiple images and arcs appear. Drag the source or lens to explore lensing geometry. The background field is computed pixel-by-pixel using the point-mass lens equation: β = θ − θE² / θ, where θE is the Einstein radius.
Click canvas to move the lens • Source moves with slider
Lens type
Parameters
Display
Stats
β = θ − (θE²/|θ|)·θ̂
Einstein radius:
θE = √(4GM·Dls/(c²·Dl·Ds))
Magnification:
μ = |u²+2| / (|u|·√(u²+4))
u = β/θE
From Prediction to Discovery
Einstein predicted light deflection by the Sun in 1915; the 1919 Eddington expedition confirmed it during a solar eclipse. The first gravitationally lensed quasar (double quasar Q0957+561) was discovered in 1979. Today gravitational lensing is one of the most powerful tools in cosmology — mapping the distribution of dark matter in galaxy clusters (the "Bullet Cluster"), measuring the Hubble constant independently, and finding exoplanets via microlensing. In the SIS model (singular isothermal sphere) the lens equation becomes β = θ − θE·sgn(θ), producing two images of equal brightness flanking the lens.