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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.^[ref]

Why can a small displacement produce a large image? For a converging thin lens, write $u_o=f_o+ϵ$ with $epsilon>0$. Substitution into the thin lens equation givesThe 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.

An optical microscope whose microscope objective, with the specimen at its designed front focal plane, sends out a parallel bundle of light rays from each specimen point. Different specimen points generally give different bundle directions. A tube lens then forms the finite intermediate microscope image; the microscope eyepiece views it. This parallel region permits suitable optical accessories to be inserted. Finite-conjugate and infinity-corrected components must be matched to their intended system.^[ref]

In the ideal paraxial approximation, an object height $h_o$ at objective focal length $f_o$ gives bundle slope $-h_o/f_o$. A tube lens of focal length $f_t$ maps that slope to $h_i=-f_t{h}_o/f_o$, soThis is a two-assembly result. Substituting infinity into the single-objective transverse magnification $-v_o/u_o$ would not describe the finite recorded image. Infinity correction concerns the region after the objective; relaxed-eye viewing concerns the region after the eyepiece. They are distinct conditions.

The real image of the specimen supplied to the microscope eyepiece or a recording surface. In the example above, a bare detector placed at $x=60\mathrm{mm}$ records an image five times the specimen's length, inverted. It does not record a fifty-times image: that number compares viewing angles under the stated reference convention. An optical camera receiving the eyepiece's outgoing light needs its own optical lens to form a further real image, with a recording scale determined by that added image formation.

An optical microscope uses light and optical lens assemblies to reveal small structures, such as the boundaries of biological cells or defects in a manufactured surface. In a compound optical microscope, the microscope objective supplies an enlarged real image; the microscope eyepiece makes that intermediate microscope image subtend a larger viewing angle. The transverse magnification of the first stage and the angular magnification of the second answer different questions.^[ref]

Consider an original ideal finite-conjugate microscope in air, with both optical lens assemblies treated as converging thin lens elements in the paraxial approximation. Choose objective focal length $f_o=10\mathrm{mm}$ and object distance $u_o=12\mathrm{mm}$. The thin lens equation and signed transverse magnification givePlace a microscope eyepiece of focal length $f_e=25\mathrm{mm}$ a further $25\mathrm{mm}$ beyond the intermediate microscope image. The objective-to-eyepiece separation is therefore $85\mathrm{mm}$. Each object point then supplies a parallel outgoing bundle of light rays, appropriate to a relaxed eye focused at infinity. Define the unaided reference as the same object viewed at distance $D=250\mathrm{mm}$; this is a rating convention, not a universal property of eyesight. The eyepiece angular magnification and total signed angular magnification areFor instance, a hypothetical object height $h_o=0.020\mathrm{mm}$ becomes $h_i=-0.100\mathrm{mm}$ at the intermediate microscope image. The signed viewing angles are approximately $h_i/f_e=-0.004\mathrm{rad}$ with the instrument and $h_o/D=0.00008\mathrm{rad}$ unaided. Their ratio is $-50$: enlarged and inverted. These are stipulated model dimensions, not measurements or specifications of a modern commercial optical microscope.

The attraction of an optical microscope is that seeing can become measuring: a stage micrometer supplies a known object-space length, and microscope scale calibration converts an image readout into a specimen length. This also separates a large-looking image from a trustworthy size estimate. Meanwhile, diffraction-limited resolution depends on numerical aperture and wavelength; empty magnification enlarges an existing blur without revealing additional structure.

A stereomicroscope is an optical microscope that sends distinct views of the same specimen to the two eyes through separate viewing channels. The views originate at slightly different directions, producing stereo disparity that supports stereoscopy. Two microscope eyepieces alone do not establish stereo imaging: splitting one image into identical copies supplies no second viewpoint.

A two-objective arrangement uses separate microscope objective assemblies whose viewing directions converge on the specimen. A shared-objective arrangement can instead preserve two distinct viewing bundles through one main objective. The distinction concerns how the two perspectives are formed, rather than the number of eyepieces. A primary manufacturer manual gives a concrete two-path example: its S-series optics have a10° convergence angle and a compact lower assembly providing access around the specimen.^[ref]

For an original geometric illustration, take two viewing rays inclined by $\pm \alpha$ to the normal of a reference plane. A feature at height $h$ above that plane has ray intersections displaced in opposite directions by $h\tan \alpha$, so their separation isWith total convergence angle $2\alpha =10^{\circ }$ and $h=1\mathrm{mm}$, the separation is about0.175mm. This back-projected reference-plane geometry illustrates stereoscopic triangulation; it is not a specification of human depth accuracy or a universal pixel-to-height calibration. Actual image coordinates also depend on each channel's optics and alignment.

The distinct viewpoints are useful when positioning a fine tool near a surface, inspecting a small mechanical assembly or distinguishing raised features from flat markings. Illumination reflected from an opaque surface makes many such specimens accessible without preparing a thin transmitting section. The microscope working distance determines how much physical room remains between the instrument and the focused specimen, which matters when a probe or tool must enter that space.

For measurement, retain the magnification setting and calibrate the relevant channel with a stage micrometer. A scale calibration in a reference plane does not automatically convert stereo displacement into height; that requires the viewing geometry or a separate height calibration. Increasing magnification also does not guarantee improved diffraction-limited resolution. The purpose of the second view is geometric information, alongside the instrument's ability to resolve and magnify structure.