= Finite-conjugate microscope
An <optical microscope> whose <microscope objective> is designed to form a <real image> at a specified finite distance. The intended image distance and <optical aberration> corrections belong together; mechanical tube length is a mounting specification, not automatically the image distance measured from a <principal plane>.<Infinity Optical Systems by Nikon Instruments Inc.>[Infinity Optical Systems, opening finite-system discussion and Fig. 2(a)]{ref}
Why can a small displacement produce a large image? For a converging <thin lens>, write $u_o=f_o+\epsilon$ with $epsilon>0$. Substitution into the <thin lens> equation gives
$$
v_o=\frac{f_o(f_o+\epsilon)}{\epsilon},\qquad m_o=-\frac{f_o}{\epsilon}.
$$
The <similar triangles> construction supplies the minus sign. The example has $epsilon=2\,\mathrm{mm}$ and hence $m_o=-5$. Letting $epsilon$ decrease moves the <real image> farther away; it does not keep the <microscope eyepiece> in focus at a fixed position. Large <transverse magnification> therefore requires the correct conjugate geometry, not merely a short <focal length>.
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