Which one of the following statements is correct about the magnificati

Which one of the following statements is correct about the magnification of an optical microscope?

Magnification increases with the increase in focal length of eyepiece
Magnification increases with the increase in focal length of objective
Magnification does not depend upon the focal length of eyepiece
Magnification decreases with the increase in focal length of eyepiece
This question was previously asked in
UPSC NDA-1 – 2017
The correct statement is that magnification decreases with the increase in focal length of eyepiece. The total magnification of an optical microscope is the product of the magnification of the objective lens and the magnification of the eyepiece.
The magnification of the eyepiece (Me) is given by Me = D/fe (when the final image is formed at infinity) or Me = 1 + D/fe (when the final image is formed at the near point, D ≈ 25 cm). In both cases, Me is inversely proportional to the focal length of the eyepiece (fe). A larger fe results in a smaller Me. Similarly, the magnification of the objective lens (Mo) is approximately inversely proportional to its focal length (f₀). Mo ≈ L/f₀, where L is the tube length.
The total magnification M = Mo * Me. Therefore, increasing the focal length of the eyepiece (fe) decreases the eyepiece magnification (Me), which in turn decreases the total magnification of the microscope. Similarly, increasing the focal length of the objective (f₀) decreases the objective magnification (Mo), also decreasing the total magnification.