Telescope Resolving Power Calculator

Resolving power (angular resolution) is the ability to distinguish two closely spaced objects as separate. The Rayleigh criterion gives the minimum angular separation: theta = 1.22 * lambda / D (in radians), where lambda is wavelength of light and D is the aperture diameter. Smaller theta means better resolution. Resolution improves with larger aperture and shorter wavelength.

The Rayleigh criterion states that two point sources are just resolvable when the central maximum of the diffraction pattern of one falls on the first minimum of the other. This gives: theta = 1.22 * lambda / D radians. For visible light at 550 nm and a 200 mm (8 inch) aperture: theta = 1.22 * 550e-9 / 0.2 = 3.35e-6 rad = 0.69 arcseconds.

Dawes' limit is an empirical formula for the resolution of a perfect telescope observing double stars under typical conditions: theta_arcsec = 116 / D_mm, where D_mm is aperture in millimeters. For a 100 mm aperture: 1.16 arcseconds. It is slightly more optimistic than the Rayleigh criterion because the human eye can detect an elongation before two Airy disks are fully separated.

Theoretical resolution (diffraction limit) is rarely achieved by ground-based telescopes because of atmospheric turbulence (seeing). Typical astronomical seeing smears images to 1-3 arcseconds at sea level, 0.5-1 arcsecond at mountain observatories. Adaptive optics systems correct for seeing and allow large telescopes to approach their diffraction limit. Space telescopes (Hubble, JWST) are not affected by atmospheric seeing.

Resolution scales with wavelength: theta = 1.22 * lambda / D. Radio telescopes need enormous apertures to compensate for long wavelengths (meters). The Very Large Array uses apertures up to 36 km via interferometry to achieve arcsecond resolution at radio wavelengths. The Event Horizon Telescope (EHT) uses Earth-sized baselines at millimeter wavelengths to achieve microarcsecond resolution, sufficient to image black hole shadows.