Rayleigh criterion: θ = 1.22λ / D, expressed in arcseconds as 138 / D(mm) at 550 nm. Dawes' empirical limit for equal-brightness visual doubles: 116 / D(mm). Limiting magnitude follows the aperture-gain relation m = 2.7 + 5·log₁₀(D) + 5·log₁₀(transmission), reduced toward the naked-eye NELM when the sky is bright. These are theory — atmospheric seeing usually sets the real limit near 1″ or worse from the ground.