= Solution
For a displayed width $D$ representing a scanned specimen width $d$, \b[the linear image <magnification> is]
$$
\boxed{M=\frac{D}{d}.}
$$
The user changes the scan-coil excursion, hence $d$. A smaller raster displayed at the same width gives larger <magnification>. Changing the display or print size also changes displayed <magnification>, so the calibrated scale bar is more portable than a <magnification> label. This is the scan/display principle described in the manufacturer's microscope guide.<Scanning Electron Microscope A To Z by JEOL>[Magnification of SEM, printed p.7: scan width and display width; the same raster-display geometry applies in STEM]{ref}
At the low-magnification extreme, the probe scans the widest accessible field. Coil range, apertures, scan distortion and maintaining focus constrain the actual usable width. Formally increasing $d$ without bound would make $M$ arbitrarily small, but a real column has a finite accessible field.
At the high-magnification extreme, the scan covers a very small region. Formally $d\to0$ makes $D/d$ diverge, but exactly zero scan width samples one location and supplies no spatial image. <Electron microscope resolution>, finite probe size, pixel spacing, drift, noise and specimen damage set the useful limit. Enlarging a field already sampled more finely than its resolvable information produces \b[<empty magnification>], not new structural detail. For $N$ pixels across a field, the specimen sampling interval is $d/N$; this is distinct from the probe's <spatial resolution>.
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