Final answer:
The spatial resolution of optical microscopy is primarily a function of the wavelength of the illumination light and the numerical aperture of the objective lens, with the numerical aperture being a crucial factor as it defines the lens's ability to gather light.
Step-by-step explanation:
The spatial resolution of optical microscopy refers to the microscope's ability to distinguish between two closely spaced points as separate entities. Two critical factors that influence resolution are the wavelength of the illumination light and the numerical aperture (NA) of the objective lens. Shorter wavelengths provide higher resolution, and a higher numerical aperture indicates a greater ability of a lens to gather light, hence improving resolution.
The numerical aperture is a particularly crucial factor because it directly correlates with the light-gathering ability of the lens. It is calculated using the angle of acceptance of light that the lens can capture and is defined as NA = n sin α, where 'n' is the refractive index and 'α' is half the acceptance angle. This means a lens with a higher numerical aperture will have a higher resolution, as it can capture more light from finer details of the specimen.