Final answer:
The largest possible numerical aperture (NA) for a microscope objective designed for use in air is 1.0, as the sine of the angle cannot exceed 1, and the refractive index of air is 1.
Step-by-step explanation:
The largest possible numerical aperture (NA) of a microscope objective designed for use in air is 1.0. The numerical aperture is a dimensionless number that represents the light-gathering ability of a lens and is related to the maximum acceptance angle for light to enter the lens. In air, the refractive index is 1, and since numerical aperture is defined as NA = n sin(θ), where n is the refractive index of the medium between the objective lens and the specimen and θ is half the acceptance angle, the maximum NA in air is 1.0 because the sine of the angle cannot exceed 1. Lenses that exceed an NA of 1.0 are called immersion lenses and require a medium between the specimen and the lens, such as oil or water, to achieve such high NAs.