Final answer:
For a microscope with a numerical aperture of 0.9, the maximum useful magnification ranges approximately between 900x and 1,350x. The provided values of a microscope resulting in 250,000x magnification are not viable as the typical upper limit for normal optical microscopes is around 1,500x.The correct answer is option D.
Step-by-step explanation:
The answer to the question regarding the maximum useful magnification of a microscope with an objective lens that has a numerical aperture of 0.9 is not provided directly in any examples mentioned. However, we can reflect on the principles that determine the maximum useful magnification of a microscope.
The maximum useful magnification of a microscope is typically around 1,000 to 1,500 times the numerical aperture. Therefore, for a numerical aperture of 0.9, the useful magnification would range approximately between 900x and 1,350x. This suggests that the answer would likely fall between option D) 450 - 900 and a value slightly higher than this range but not as high as the options suggesting magnifications in the range of several thousands.
Regarding the scenario presented about a microscope with a 0.500 cm focal length objective lens and a 5.00 cm focal length eyepiece resulting in an overall magnification of 250,000, this is not a viable value. Normal optical microscopes usually have a maximum magnification around 1,500x due to limitations such as diffraction.