 Solution

A finite optical pupil spreads a point into a point spread function. In incoherent imaging an extended intensity distribution is convolved with that function; its Fourier transform is the optical transfer function, which attenuates and ultimately removes high spatial frequencies. For an ideal circular pupil the point response is an Airy disk. The Rayleigh criterion for two equally bright incoherent points isA microscope's object-space scale is of order $\lambda /(2\mathrm{NA})$, with the numerical factor depending on illumination and the criterion; $\mathrm{NA}=n\sin \alpha$ measures the accepted ray cone. A larger pupil or shorter wavelength improves the diffraction scale. Aberrations, defocus, detector pixel sampling, motion, background and photon noise can worsen practical performance. Merely magnifying the same blurred image adds no information. Coherent sources require amplitude superposition instead of the incoherent intensity rule. Rayleigh resolution is a convention for separating a pair, distinct from the precision of localizing one isolated point; information does not abruptly vanish below it.