Diffraction blurs every image: two point sources closer than the angular resolution merge into one blob. Bigger apertures and shorter wavelengths see finer detail – which is why astronomers build huge telescopes and why electron microscopes beat light microscopes.
How to use the Angular Resolution Calculator
- Wavelength λ
- Aperture diameter D
- Distance to the object (optional)
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the wavelength and the aperture diameter. Visible light is about 550 nm. The linear detail resolvable at a given distance is the angle times the distance.
Tips
- Use the sign convention of the formula: real images and distances are positive in most lens equations.
- Wavelength units matter – nm for visible light, µm for infrared.
- Refractive index of air is about 1.000293; vacuum is exactly 1.
- Angles are measured from the normal to the surface.
Common mistakes to avoid
- Measuring angles from the surface instead of the normal.
- Mixing focal length in mm and object distance in m.
- Forgetting that a diverging lens has a negative focal length.
Inputs explained
| Field | What to enter |
|---|---|
| Wavelength λ | Units: nm, µm, mm, m, pm, Å |
| Aperture diameter D | Units: mm, cm, m, in, µm |
| Distance to the object (optional) | Units: km, m, mi, nmi, ft |
What each result means
- Angular resolution θ = 1.22×[Wavelength λ]÷[Aperture diameter D]
- In arcseconds = deg([Angular resolution θ])×3600
- In degrees = deg([Angular resolution θ])
- Smallest detail at that distance = [Angular resolution θ]×[Distance to the object (optional)]
Example values
How the main result changes when Wavelength λ changes and everything else stays at the example values above:
| Wavelength λ (nm) | In arcseconds (″) |
|---|---|
| 275 | 0.692 |
| 412.5 | 1.038 |
| 550 | 1.384 |
| 687.5 | 1.73 |
| 825 | 2.0761 |
| 1,100 | 2.7681 |
Formula
θ = 1.22 · λ / DWorked example
Inputs — Wavelength λ: 550 nm; Aperture diameter D: 100 mm; Distance to the object (optional): 384,400 km.
Results — Angular resolution θ = 0.00000671 rad; In arcseconds = 1.384 ″; In degrees = 0.00038445 °; Smallest detail at that distance = 2,579.324 m.
Key terms
- Diffraction limit
- The best resolution an aperture can achieve.
Frequently asked questions
What is the Rayleigh criterion?
Two points are just resolved when one's central maximum falls on the other's first minimum.
What is the resolution of the human eye?
About 1 arcminute in practice (diffraction limit ≈ 20″ for a 6 mm pupil).
Why do radio telescopes need to be huge?
Radio wavelengths are long, so a large D is needed for fine resolution.
Can resolution beat the diffraction limit?
Super-resolution microscopy techniques can, but ordinary optics cannot.
What formula does the Angular Resolution Calculator use?
θ = 1.22 · λ / D.