Gravitational Lensing

Light Bending & Einstein Rings

Point-Mass Lens Drift

Foreground lensStellar images (tangentially stretched)Einstein radius θ_E (dashed)

Key Parameters

Lens equation

θ² − βθ = θ_E²

Einstein radius

θ_E ∝ √(M)

Solar limb

1.75″

Cluster scale

10 – 50″

Microlensing

μas – mas

Image count

2 (point lens)

What's Happening

Light follows null geodesics — straight lines through curved spacetime. A mass curves spacetime, so a ray skimming past it deflects by an angle α = 4GM / (c² b), where b is the impact parameter.

For a point mass, every background source has two images: one outside the Einstein radius (slightly stretched tangentially) and one inside (faint, inverted). As source-lens-observer alignment improves, both images merge onto a single circle — the Einstein ring.

Real galaxy or cluster lenses can produce four images, giant arcs, and richly distorted background-galaxy maps — the patterns reveal both luminous and dark mass within the lens.

Why It Matters

First experimental confirmation of GR (Eddington, 1919)

Maps total mass — including dark matter — in clusters

Magnifies distant galaxies, acting as a cosmic telescope

Time delays between images constrain the Hubble constant

Microlensing detects exoplanets and dark compact objects

Black-hole shadows are extreme self-lensing events

Where We See It

Eddington's eclipse (1919)

1.75″ deflection

During a total solar eclipse, Eddington's expedition photographed stars near the Sun's limb and measured their apparent shift — 1.75 arcseconds, exactly Einstein's prediction. The result made global headlines and turned general relativity from a curiosity into accepted physics overnight.

Twin Quasar Q0957+561

First strong lens, 1979

Discovered in 1979, this was the first confirmed multi-image gravitational lens — two images of the same quasar separated by 6 arcseconds, lensed by an intervening galaxy. The two images vary identically with a ~417-day delay, the time difference along the two light paths.

Cluster arcs (Abell 2218 etc.)

Strong cluster lensing

Massive galaxy clusters lens distant background galaxies into spectacular blue arcs and arclets. The pattern of distortion maps the cluster's total mass — including dark matter — and lets us reconstruct sources that would otherwise be too faint to see.

Microlensing exoplanets

Brief brightness spike

When a foreground star with a planet passes in front of a background star, the resulting brightness curve has a characteristic spike from the planet's lensing contribution. Surveys like KMTNet have used this to discover thousands of planets, including ones at orbits Kepler can't reach.