 Solution

Under the Rayleigh criterion, two equally bright, mutually incoherent point sources are just resolved when the central maximum of one diffraction pattern lies at the first minimum of the other. Their intensities, rather than their electric-field amplitudes, add. For an ideal circular aperture of diameter $D$, the first dark ring of the Airy disk givesThe angle is in radians in the small-angle limit. This is a conventional resolution criterion for a specified aperture and wavelength; it is not an absolute prohibition on estimating a source separation by fitting noisy data under additional assumptions.