Gravitational Lensing
Gravitational lensing is the bending and focusing of light from a distant source by the gravitational field of an intervening massive object (the lens), as predicted by Einstein's general theory of relativity. The degree of bending depends on the mass of the lensing object and the geometry of the source-lens-observer alignment, producing phenomena ranging from subtle shape distortions (weak lensing) to dramatic arcs and multiple images (strong lensing) and point-source brightening (microlensing). Gravitational lensing is a key tool for mapping dark matter distributions, measuring the Hubble constant, and discovering exoplanets.
Key Formula
θ = 4GM / (c² × b)
LaTeX: \theta = \frac{4GM}{c^2 b}
| Symbol | Meaning | Unit |
|---|---|---|
| θ | Deflection angle of light | radians |
| G | Gravitational constant (6.674 × 10⁻¹¹) | N·m²/kg² |
| M | Mass of the lensing object | kg |
| c | Speed of light (3 × 10⁸) | m/s |
| b | Impact parameter (closest approach distance) | m |
Worked Example
Problem
Calculate the deflection angle of starlight grazing the surface of the Sun (M_Sun = 1.989 × 10³⁰ kg, R_Sun = 6.96 × 10⁸ m) as measured by Einstein's general relativity formula.
Solution
Using θ = 4GM / (c²b), where b = R_Sun (light just grazes the solar surface): θ = 4 × (6.674 × 10⁻¹¹) × (1.989 × 10³⁰) / [(3 × 10⁸)² × (6.96 × 10⁸)] Numerator: 4 × 6.674 × 10⁻¹¹ × 1.989 × 10³⁰ = 5.309 × 10²⁰ Denominator: (9 × 10¹⁶) × (6.96 × 10⁸) = 6.264 × 10²⁵ θ = 5.309 × 10²⁰ / 6.264 × 10²⁵ = 8.474 × 10⁻⁶ radians Converting to arcseconds: θ = 8.474 × 10⁻⁶ × (180/π) × 3600 ≈ 1.748 arcseconds
Answer
Deflection angle θ ≈ 1.75 arcseconds, confirmed by Eddington's 1919 solar eclipse expedition.
Types of Gravitational Lensing and Their Applications
| Type | Lens Mass | Observable Effect | Application |
|---|---|---|---|
| Strong lensing | Galaxy clusters (10¹⁴–10¹⁵ M_Sun) | Arcs, Einstein rings, multiple images | Dark matter mapping |
| Weak lensing | Large-scale structure | Statistical shape distortions | Cosmic shear surveys |
| Microlensing | Stars, planets (0.1–100 M_Sun) | Transient brightening | Exoplanet detection |
| Self-lensing | Compact objects (BH, NS) | Magnification of background | Binary systems |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Dark Matter
Dark matter is a hypothetical form of matter that does not interact with the electromagnetic force, making it invisible to the entire electromagnetic spectrum, yet its existence is inferred from its gravitational effects on visible matter, radiation, and the large-scale structure of the universe. It is estimated to constitute approximately 27% of the total mass-energy content of the universe, compared to only 5% for ordinary baryonic matter. Leading candidates include Weakly Interacting Massive Particles (WIMPs), axions, and sterile neutrinos, though no direct detection has been confirmed as of 2025.
General Relativity
General relativity is Albert Einstein's geometric theory of gravitation, published in 1915, which describes gravity not as a force but as the curvature of spacetime caused by mass and energy. Massive objects warp the fabric of spacetime, and other objects follow curved paths (geodesics) through this warped spacetime, which we perceive as gravitational attraction. The theory has been confirmed by numerous observations including gravitational lensing, gravitational redshift, the precession of Mercury's orbit, and the detection of gravitational waves.
Hubble's Law
Hubble's Law is the empirical observation that the recession velocity of a galaxy is directly proportional to its distance from the observer, expressed as v = H₀d, where H₀ is the Hubble constant. First published by Edwin Hubble in 1929 based on measurements of galaxy redshifts, it provided the first direct observational evidence for the expanding universe predicted by general relativity. The Hubble constant H₀, currently estimated at approximately 67–73 km/s/Mpc from different methods, also allows astronomers to estimate the age of the universe as roughly 1/H₀.
"Gravitational" from Latin "gravitas" (heaviness, weight) and "gravitatio." "Lensing" from Latin "lens" (lentil), as optical glass lenses were named for their lentil-like shape. The phenomenon was predicted by Einstein in 1915 (general relativity) and first confirmed by Arthur Eddington during the 1919 solar eclipse.