Angular Resolution Calculator
Calculate the minimum angular separation that can be resolved by an optical instrument using the Rayleigh criterion
Common values: 550 nm = 0.00000055 m (visible light)
The diameter of the lens or mirror aperture
How to Use This Calculator
Enter the Wavelength
Input the wavelength of light in meters. For visible light, use values around 0.00000055 m (550 nm). You can convert nanometers to meters by dividing by 1,000,000,000.
Enter the Aperture Diameter
Input the diameter of the optical instrument's aperture (lens or mirror) in meters. For example, a 10 cm telescope would be 0.1 meters.
Calculate
Click the "Calculate Angular Resolution" button to get the minimum angular separation in arcseconds that your instrument can resolve.
Formula
θ = 1.22 × (λ / D)
Where:
- θ = Angular resolution (in radians)
- λ = Wavelength of light (in meters)
- D = Diameter of the aperture (in meters)
- 1.22 = Constant derived from the first zero of the Bessel function (Rayleigh criterion)
To convert to arcseconds: Multiply radians by 206,265
Example Calculation:
For a telescope with 0.1 m (10 cm) aperture observing at 550 nm wavelength:
λ = 0.00000055 m, D = 0.1 m
θ = 1.22 × (0.00000055 / 0.1) = 0.00000671 radians
θ = 0.00000671 × 206,265 = 1.38 arcseconds
About Angular Resolution Calculator
Angular resolution is a fundamental concept in optics that determines the smallest angular separation between two point sources that can be distinguished as separate by an optical instrument. This calculator uses the Rayleigh criterion, which states that two point sources are just resolvable when the center of the diffraction pattern of one source is directly over the first minimum of the diffraction pattern of the other.
When to Use This Calculator
- Telescope Design: Determine the resolution capabilities of telescopes for astronomical observations
- Camera Lens Selection: Calculate the angular resolution of camera lenses to understand image quality
- Microscope Specifications: Evaluate the resolving power of microscopes for biological or material science applications
- Optical System Design: Plan optical systems by understanding resolution limitations based on aperture size
- Educational Purposes: Learn about diffraction limits and the physics behind optical resolution
Why Use Our Calculator?
- ✅ Instant Results: Get accurate angular resolution calculations immediately
- ✅ Easy to Use: Simple interface requiring only wavelength and aperture diameter
- ✅ Automatic Unit Conversion: Results displayed in both radians and arcseconds
- ✅ 100% Free: No registration or payment required
- ✅ Educational: Includes formula explanations and worked examples
- ✅ Mobile Friendly: Works perfectly on all devices
Common Applications
Astronomy: Astronomers use angular resolution calculations to determine what features can be observed with different telescopes. The Hubble Space Telescope, with its 2.4-meter aperture, can resolve objects separated by about 0.05 arcseconds at visible wavelengths.
Photography: Camera manufacturers and photographers calculate angular resolution to understand lens sharpness and to compare different lens options. Higher resolution means finer detail can be captured.
Microscopy: In biological and materials research, angular resolution determines the smallest features that can be distinguished, which is crucial for examining cells, tissues, or material structures.
Tips for Best Results
- Use consistent units (meters for both wavelength and diameter)
- For visible light, typical wavelengths range from 400 nm (0.0000004 m) to 700 nm (0.0000007 m)
- Remember that atmospheric turbulence can limit practical resolution to worse than the theoretical limit
- Larger apertures provide better resolution, but also increase cost and complexity
- For astronomical observations, consider using adaptive optics to approach the theoretical resolution limit
Frequently Asked Questions
What is the Rayleigh criterion?
The Rayleigh criterion is a standard for determining when two point sources can be resolved. It states that two sources are just resolvable when the center of one diffraction pattern coincides with the first minimum of the other pattern. The constant 1.22 comes from the mathematics of circular apertures.
Why does wavelength affect angular resolution?
Shorter wavelengths produce less diffraction, resulting in smaller diffraction patterns and better resolution. This is why electron microscopes (using very short wavelength electrons) can achieve much higher resolution than light microscopes.
Can I achieve better resolution than the calculated value?
The Rayleigh criterion represents the theoretical limit for conventional optics. In practice, atmospheric conditions, optical quality, and other factors often limit resolution to worse values. However, techniques like adaptive optics, interferometry, or super-resolution microscopy can sometimes exceed the classical limit.
How does aperture size affect resolution?
Larger apertures provide better (smaller) angular resolution because they collect more light and produce narrower diffraction patterns. This is why large telescopes are needed to resolve fine details in astronomical objects.
What's the difference between angular resolution and spatial resolution?
Angular resolution is the minimum angular separation between two resolvable points. Spatial resolution is the actual physical distance between resolvable points, which depends on the distance to the object. For example, 1 arcsecond resolution at 1 km distance corresponds to about 4.8 mm spatial resolution.