Calculate the minimum angular separation between two objects that can be distinguished using the Rayleigh criterion.
Angular resolution is the ability of an optical system to distinguish between two closely spaced objects as separate entities. It defines the minimum angular separation required to resolve two point sources.
The Rayleigh criterion is the standard defining angular resolution. Two point sources are just resolved when the central maximum of one diffraction pattern coincides with the first minimum of the other. This theoretical limit is determinedby wavelength and aperture size.
Larger instruments and shorter wavelengths provide better resolution, which is why telescopes are so large and electron microscopes achieve such magnification.
Where: θ = angular resolution (rad), λ = wavelength (m), D = aperture diameter (m), 1.22 = Bessel function constant
Telescope with 1 meter mirror observing visible light (550 nm)
Larger D means smaller θ (better resolution). This is why professional telescopes have such large mirrors.
Yes, shorter λ yields smaller θ. Ultraviolet telescopes see finer details than infrared; electron microscopes beat optical microscopes.
It's the first zero of the Bessel function J₁, derived from wave diffraction theory for circular apertures.
Not with individual apertures. Advanced interferometry combines light from multiple telescopes to achieve better effective resolution.
Related Tools
Calculate aperture area.
Calculate Brewster's angle.
Calculate Compton scattering.
Calculate Compton wavelength.
Calculate lens vertex distance.
Calculate de Broglie wavelength.