= Empty magnification
<Empty magnification> enlarges an image without revealing additional specimen detail. Adequate <angular magnification> can make existing detail visible to the eye, but it cannot undo the objective's <diffraction> blur. For equally bright, mutually incoherent <optical point sources> and an ideal circular <optical pupil>, a commonly used lateral <Rayleigh criterion> in object space is
$$
d_{\rm R}\simeq\frac{0.61\lambda}{\mathrm{NA}},\qquad \mathrm{NA}=n\sin\alpha,
$$
where $\lambda$ is the vacuum <wavelength>, $n$ is the specimen-medium <refractive index>, and $\alpha$ is the admitted half-<angle>. For this model, $\lambda=550\,\mathrm{nm}$ and $\mathrm{NA}=0.25$ give $d_{\rm R}\simeq1.342\,\mathrm{\mu m}$; changing only <numerical aperture> to $0.50$ gives $0.671\,\mathrm{\mu m}$. Changing only the eyepiece leaves this object-space scale unchanged. Illumination, <optical coherence>, <optical aberrations> and specimen visibility matter in real instruments; this criterion is not a universal threshold.<Resolution by Michael W. Davidson>[Formula 2, discussion after Formulas 1–3 and final resolving-power paragraph]{ref}
The geometric reason is especially simple. If a fixed recorded image is enlarged by a factor $q>0$, a feature separation $s$ and a blur width $b$ become $qs$ and $qb$. Their ratio remains
$$
\frac{qs}{qb}=\frac{s}{b}.
$$
This is the lower-panel construction in the diagram. A change to the <microscope objective> can change <numerical aperture> and hence the specimen detail captured; a display zoom changes how large that captured detail looks. <Microscope scale calibration>, <diffraction-limited resolution> and <angular magnification> are three complementary properties to report.
Back to article page
