Equations · equation

Rayleigh Criterion

Waves & Optics · 1879

Equation
θ ≈ 1.22 λ / D
Field
Waves & Optics
Named After
Lord Rayleigh
Symbols
θ the smallest angle two points can be apart and still be told apart · λ wavelength · D aperture diameter
Year
1879

Significance

The finest detail any telescope, microscope or eye can resolve is set by wavelength over aperture — diffraction, not workmanship, is the floor. The 1.22 is the first dark ring of the Airy pattern that a circular aperture makes; a slit or a square would carry a different constant. It is why telescopes are big, why radio dishes are enormous and then combined into interferometers to fake a bigger one, and why no visible-light microscope will ever show an atom. It is also why JWST is not sharper than Hubble: working at 2 μm instead of 500 nm costs a factor of four, and 6.5 m of mirror against 2.4 m buys back less than three, so JWST resolves about 0.08″ where Hubble manages 0.05″ and would need a 9.6 m mirror to match it. What the infrared buys is not sharpness — it is seeing through dust, and seeing light so redshifted that Hubble cannot see it at all.

Instruments

Requires

Referenced by

equation
instrument

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From the Equations database in Notion, last edited 2026-08-26. This page is the row, rendered by the build; nothing on it is written by hand.