Final answer:
The maximum useful magnification of a microscope with an objective lens NA of 0.9 is 900x. This is calculated by multiplying the NA by 1000, which aligns with the resolution limits of standard optical microscopes.
Step-by-step explanation:
The maximum useful magnification of a microscope can be estimated by the formula:
Maximum Useful Magnification = NA × 1000
Therefore, with an objective lens that has a numerical aperture (NA) of 0.9, the maximum useful magnification is:
900x (0.9 × 1000).
It’s important to note that exceeding this magnification often leads to empty magnification, where the image appears larger but no additional detail is resolved. This is largely due to the theoretical resolution limit of the microscope, which is typically around -0.2 μm for normal optical microscopes using visible light.