Past exam of the physics A course of the University of Cambridge / 2017 / Paper 2 / Section A / 2 / Solution

For an object near the front focal plane, the objective's numerical aperture in air isThe Rayleigh criterion for a circular objective gives object-space diffraction-limited resolutionThe factor $1.22$ comes from the first zero of the Airy disk. Using the exact $\sin (\arctan (D/(2f)))$ changes the result by less than $1\%$. A coarser $\lambda f/D$ estimate gives $2.4\mu \mathrm{m}$; the chosen criterion must be stated. This estimates the aperture limit, before aberrations and detector sampling.