Angular Resolution Calculator
Calculate the angular resolution of optical instruments using the Rayleigh criterion
Calculate Angular Resolution
Light wavelength (Green)
Lens or mirror diameter
Quick Wavelength Presets:
Calculation Results
Rayleigh Criterion: θ = 1.22 × λ / d
• θ = 1.22 × 5.50e-7 / 5.00e-3 = 1.342e-4 rad
Linear Resolution at Distance
Example Calculation
Human Eye vs Hubble Telescope
Human Eye: d = 2 mm, λ = 550 nm (green light)
Hubble Telescope: d = 2.4 m, λ = 550 nm
Solution
Human Eye: θ = 1.22 × 550×10⁻⁹ / 0.002 = 3.355×10⁻⁴ rad ≈ 69 arcsec
Hubble: θ = 1.22 × 550×10⁻⁹ / 2.4 = 2.796×10⁻⁷ rad ≈ 0.058 arcsec
Improvement: Hubble is ~1200 times better than human eye!
Angular Resolution Concepts
Typical Angular Resolutions
Understanding Angular Resolution
What is Angular Resolution?
Angular resolution is the ability of an optical instrument to distinguish small details or separate two objects that appear close together. It represents the smallest angle between two point sources that can be resolved as separate objects.
Rayleigh Criterion
- •θ = 1.22λ/d - Basic Rayleigh formula
- •Based on diffraction through circular aperture
- •First minimum coincides with central maximum
- •Fundamental limit due to wave nature of light
Applications
θ = 1.22λ/d
- θ: Angular resolution (radians)
- λ: Wavelength of light (meters)
- d: Aperture diameter (meters)
- 1.22: Constant for circular aperture
Key Insight: Larger apertures and shorter wavelengths provide better (smaller) angular resolution.
Practical Notes:
• 1 arcsec = 1/3600 degree
• Atmospheric seeing limits ground telescopes to ~1 arcsec
• Space telescopes achieve diffraction-limited performance