Resolving Power Calculator

Resolving power sets the limit on how fine a detail an optical instrument can distinguish. It is set by diffraction — larger apertures and shorter wavelengths give better resolution.

🔍 Optics📐 θ = 1.22λ/D🔭 Telescopes
Aperture D (m)
Wavelength λ (nm)
Please enter valid values.

Formula & Reference

VariableSymbolFormulaUnits
Angular Resolutionθθ = 1.22λ/Drad
Min Resolution (Microscope)dd = 1.22λ/(2 NA)m
ApertureDDiameter of lens/mirrorm
Numerical ApertureNAn sin(α)—

Step-by-Step Examples

Example 1
Human Eye

Pupil D=5 mm, lambda=550 nm.

  • theta = 1.22 * 550e-9 / 0.005 = 1.34e-4 rad = 27.6 arcsec
✓ Eye resolves ~1 arcminute under ideal conditions
Example 2
Hubble Telescope

D=2.4 m, lambda=550 nm.

  • theta = 1.22 * 550e-9 / 2.4 = 2.8e-7 rad = 0.058 arcsec
✓ 0.058 arcsec — Hubble resolution from space
Example 3
Microscope

D=1 cm objective, NA=0.65, lambda=550 nm.

  • d = 1.22 * 550e-9 / (2*0.65) = 516 nm = 0.52 um
✓ ~0.5 um minimum feature resolved

Real-World Applications

🔭
Astronomical Telescopes
Larger mirrors (up to 30m for ELT) give better angular resolution to study distant galaxies.
🔬
Optical Microscopy
Numerical aperture (NA) and wavelength set the 200 nm diffraction limit of visible-light microscopes.
📷
Camera Optics
Lens aperture limits resolution; diffraction competes with pixel size and aberrations.
🛰️
Spy Satellites
KH-11 type satellites with ~2.4 m mirrors achieve ~0.1 m ground resolution at 300 km altitude.

Common Mistakes to Avoid

⚠️
Rayleigh criterion is a convention

Other criteria exist (Sparrow, Abbe). Rayleigh criterion (first minimum of one coincides with center of other) is most common.

⚠️
Wavelength in medium

In a medium with n>1, effective wavelength is lambda/n. This is why oil-immersion microscopes improve resolution.

⚠️
Larger aperture always better?

Not always — atmospheric seeing limits ground-based telescopes. Adaptive optics corrects this; space avoids it.

Frequently Asked Questions

What is the Rayleigh criterion? ▾
Two point sources are just resolved when the central maximum of one diffraction pattern falls on the first minimum of the other. Gives theta = 1.22*lambda/D.
Why 1.22? ▾
It comes from the first zero of the Bessel function J1, which describes diffraction from a circular aperture. 1.22 = 1.2196... from Bessel function theory.
What limits microscope resolution? ▾
For optical microscopes: d_min = lambda/(2*NA). With NA~1.4 (oil immersion) and lambda=400 nm: d_min ~143 nm. Electron microscopes use shorter wavelength.
What is super-resolution microscopy? ▾
Techniques like STORM and PALM use fluorescence to exceed the diffraction limit, achieving 20-50 nm resolution. Nobel Prize in Chemistry 2014.
How does atmosphere limit telescope resolution? ▾
Atmospheric turbulence (seeing) limits ground telescopes to ~0.5-1 arcsec regardless of aperture. Adaptive optics corrects distortions in real time.

Related Physics Calculators

🔭 Telescope Magnification🔬 Microscope Magnification🌈 Diffraction Grating🔍 Lens Power🔍 Refractive Index

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