In a compound microscope, the focal length of the objective is f_o...

For a compound microscope to function properly and provide magnification, the objective lens must form a real, inverted, and magnified image of the object.

This requires the object to be placed between the principal focus and the center of curvature of the objective lens. Therefore, the object distance $u$ must satisfy:

$f_o < u < 2f_o$

For a real and magnified image, the image distance $v_o$ from the objective lens must be greater than $2f_o$:

$v_o > 2f_o$

The total separation $L$ between the objective and the eyepiece is the sum of the image distance from the objective and the object distance for the eyepiece ($u_e$):

$L = v_o + u_e$

Since $u_e > 0$ and $v_o > 2f_o$, we get:

$L > 2f_o$

Also, since $u < 2f_o$ and $L > 2f_o$, it strictly follows that:

$L > u$