Final answer:
The largest theoretical numerical aperture (NA) for a lens in air is 1.00. However, immersion lenses can achieve NAs greater than 1.00 by using fluids like oil with higher refractive indices to enhance light-gathering ability and resolution.
Step-by-step explanation:
The largest theoretically possible numerical aperture (NA) for an objective lens designed for use in air is 1.00. The NA is derived from the formula NA = n sin α, where n is the refractive index of the medium in which the lens is working and α is the half angle of the maximum cone of rays that can enter the lens. In air, the refractive index (n) is 1, and since the sine of an angle cannot exceed 1, the maximum NA in air is also 1. However, by using immersion lenses with fluids such as oil, glycerine, or water, which have refractive indices greater than that of air, NAs larger than 1.00 can be achieved. Immersion mediums minimize the refractive index mismatch and allow for a greater light-gathering ability and improved resolution.