• Tags: circular-aperture, Airy-disc, resolution
• Difficulty: Moderate

A circular aperture of diameter D produces an Airy pattern: a central bright disc surrounded by alternating dark and bright rings. The first dark ring (first minimum) is at sinθ = 1.22λ/D. This defines the Airy disc. The Rayleigh criterion for resolution: two point sources are just resolved when the central maximum of one coincides with the first minimum of the other. This gives the minimum angular separation θ_min = 1.22λ/D. Telescope resolving power = $\frac{D}{1.22λ}$, microscope resolving power = 2nsinα/(1.22λ). Larger apertures and shorter wavelengths improve resolution.