Final answer:
The NA of microscope lenses and optical fibers both indicate their light-gathering abilities but will vary depending on specific designs and applications, so neither is inherently larger than the other.
Step-by-step explanation:
The numerical aperture (NA) of a microscope objective lens and that of an optical fiber can vary and serve different purposes respectively. In a microscope, the NA is crucial as it indicates the light-gathering ability of the lens and consequently its resolving power.
A higher NA means the lens can resolve finer details and produce a brighter image due to its ability to collect more light. This light-gathering is related to the size of the cone of light that the lens can accept, which means better information for image formation and greater resolving power.
Optical fibers also have a numerical aperture, which is determined by the angle at which light is accepted into the fiber.
The numerical aperture in optical fibers can also be made larger than 1.00 using immersion techniques, similar to those used in microscopes to increase resolution by using a medium like oil, glycerine, or water to minimize refractive index mismatches. Whether the NA of a microscope or an optical fiber is larger is not inherent to the device itself but rather depends on the specific design and application.