Calculator inputs
Pick a mode, enter known values, and calculate the missing resolution distance quantity.
Plotly graph
The chart shows how minimum resolvable separation changes as observation distance changes while angular resolution stays fixed.
Formula used
Here, s is linear separation, θ is angular resolution in radians, R is observation distance, λ is wavelength, n is refractive index, and A is aperture diameter. For most optics work, θ is small enough that the small-angle relation is highly accurate.
How to use this calculator
- Choose the mode that matches your known values.
- Enter angular resolution directly, or derive it from wavelength and aperture.
- Set the observation distance or target separation using the most convenient units.
- Add refractive index when working in media other than air or vacuum.
- Click Calculate to show the result summary above the form.
- Review the graph, compare exact versus approximate separation, then export the result as CSV or PDF.
Example data table
| Scenario | Wavelength | Aperture | Distance | Angular resolution | Minimum separation |
|---|---|---|---|---|---|
| Small telescope viewing a target | 550 nm | 100 mm | 1,000 m | 1.38 arcsec | 6.71 mm |
| Binocular objective at mid range | 550 nm | 40 mm | 500 m | 3.46 arcsec | 8.39 mm |
| Microscope-style lens spacing check | 500 nm | 5 mm | 50 mm | 25.16 arcsec | 6.10 µm |
| Inspection optic on a short bench | 632 nm | 25 mm | 2 m | 6.36 arcsec | 61.68 µm |
FAQs
1. What does angular resolution mean?
Angular resolution is the smallest angle between two points that an optical system can distinguish as separate. Smaller values mean finer detail can be resolved at the same observation distance.
2. Why does the calculator use the Rayleigh criterion?
The Rayleigh criterion is a common diffraction-based estimate for circular apertures. It gives a practical limit for telescopes, lenses, sensors, and many classroom optics problems.
3. Why does a larger aperture improve resolution?
A larger aperture reduces diffraction spreading, which lowers the minimum resolvable angle. That smaller angle translates into a smaller linear separation at the same distance.
4. How does wavelength affect the result?
Shorter wavelengths generally improve diffraction-limited resolution because the Rayleigh angle is directly proportional to wavelength. Blue light resolves slightly finer detail than red light under equal conditions.
5. When should I use the exact trigonometric separation?
Use the exact expression when the angle becomes relatively large. For very small angles, the difference from s = θR is tiny, so the approximation is usually sufficient.
6. What unit is best for angular resolution?
Astronomy often uses arcseconds, engineering may use radians or milliradians, and microscopy may use microradians. Pick the unit that matches your source data or reporting standard.
7. Can I use this for microscopes and telescopes?
Yes. The same angular and diffraction principles apply to microscopes, telescopes, cameras, inspection optics, and many imaging systems, provided the assumptions fit the setup.
8. What does refractive index change here?
Refractive index changes the effective wavelength in the medium. Higher index lowers the wavelength inside that medium, which can reduce the diffraction-limited angle in this simplified model.