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An autocollimator is an optical instrument that measures small angular changes by sending collimated light toward a reflector and examining the returning image. The outgoing and returning paths share optical components: a beam splitter directs light from an illuminated reticle through a collimator, while the reflected light is imaged onto a detector or viewed through an eyepiece. The measurement uses autocollimation, the return of the instrument's own projected light.^[ref][ref]

A small tilt $\theta$ of a plane mirror changes the reflected beam direction by $2\theta$. In an ideal paraxial model with focal length $f$, the return-image displacement from its zero position iswith the angle in radians. For the independently chosen values $f=200\mathrm{mm}$ and $x=4\mu \mathrm{m}$, the mirror tilt is $10\mu \mathrm{rad}$, about 2.063 arcseconds. The reflected beam turns through twice that angle: confusing mirror tilt with beam deflection introduces a factor-of-two error.

A mechanical application turns angular readings into height differences. A mirror carried on two supports separated by a base $b$ has height difference $h=b\tan \theta$ across that base. With an illustrative $b=100\mathrm{mm}$ and the tilt above, $h$ is about 1 micrometre. A series of such local slopes can constrain straightness, provided the support geometry and reference are accounted for.^[ref]

The instrument therefore senses orientation through image position. It is not directly a distance gauge: lateral translation of an ideal plane mirror without tilt does not encode that translation in the same angular reading. Zero setting, measurement calibration and optical alignment remain part of interpreting the observation.