The ratio of the focal length of the objective to the focal length of the eyepiece is greater than one for

In optical instruments, the ratio of the focal length of the objective ($f_o$) to the focal length of the eyepiece ($f_e$) determines the angular magnification. For a telescope, the magnification is given by $M = f_o / f_e$. To achieve high magnification of distant objects, telescopes are designed with a long focal length objective and a short focal length eyepiece, making the ratio $f_o / f_e > 1$. For example, a telescope might have a 1500mm objective and a 25mm eyepiece. Conversely, in a compound microscope, the objective has a very short focal length to produce a high linear magnification of a nearby object, while the eyepiece has a relatively larger focal length to further magnify that image. Therefore, in a microscope, the ratio $f_o / f_e$ is typically less than one, whereas for a telescope, it is greater than one.