How to read the Zoom ladder
Updated
Under the short answer of every entry sits a horizontal ladder. Its left end is 10 cm, about the width of a hand; each rung to the right is a tenth of the one before, down to 0.1 nm, the scale of a single atom. The entry's subject sits in a round marker, like the field of view in a microscope eyepiece.
The ten rungs
| Rung | Size | Written as |
|---|---|---|
| 1 | 10 cm | 10−1 m |
| 2 | 1 cm | 10−2 m |
| 3 | 1 mm | 10−3 m |
| 4 | 0.1 mm (100 µm) | 10−4 m |
| 5 | 10 µm | 10−5 m |
| 6 | 1 µm | 10−6 m |
| 7 | 0.1 µm (100 nm) | 10−7 m |
| 8 | 10 nm | 10−8 m |
| 9 | 1 nm | 10−9 m |
| 10 | 0.1 nm | 10−10 m |
Milli (m) is a thousandth of a metre, micro (µ) a millionth and nano (n) a billionth, so 1 mm is 1,000 µm and 1 µm is 1,000 nm.
What the label in brackets means
The first time a subject's size appears, it carries a label such as [10−4 m]: the power of ten of the size in metres. A subject 0.3 mm long is 3 × 10−4 m, so its label is [10−4 m] and it sits on the fourth rung; a range gets both ends, so 20–200 µm is [10−5–10−4 m]. The label gives the rung; the exact size and its source are in the same sentence and in the Bench card.
The two dashed lines
Two dashed lines cross every ladder.
Naked eye, about 0.1 mm. Robert Hooke reckoned the naked eye could not resolve detail finer than one minute of arc, a sixtieth of a degree, as quoted in de Jong's 2024 history of visual-acuity testing. Seen from 25–40 cm, a viewing distance chosen by this site, one minute of arc spans about 73–116 µm (computed). The line is a guide, not a wall: it moves with viewing distance, with the contrast between object and background, and with the viewer's eyesight.
Some ladders carry a band for a human hair, typically 50–100 µm across by Li and colleagues' 2023 figure: the fifth and fourth rungs, up to the naked-eye line.
Light microscope, about 0.2 µm. A visible-light microscope cannot separate two points closer than a limit set by the wavelength of the light and the light-gathering power of the lens. The usual expression is Abbe's limit of 1873, d = λ / (2 NA), with λ the wavelength and NA the numerical aperture of the objective, as a 2021 methods review by Valli and colleagues gives it; for a standard fluorescence microscope detecting light of 470–700 nm, the review puts the limit at around 170–250 nm.
The line on the ladder is this site's own figure: with green light of about 550 nm and an oil-immersion objective with NA about 1.4, d = 550 nm / 2.8, about 196 nm, or about 0.2 µm (computed). The same formula moves the line: a smaller NA or a longer wavelength pushes the limit to larger sizes, a shorter wavelength pulls it down.
Why the ladder is logarithmic
On an ordinary ruler, equal distances mean equal differences in size. Lay the ten rungs on one 10 cm long and the 1 mm rung sits a hundredth of the way from the zero end, the 1 µm rung a hundred-thousandth, and every rung below lands on that same spot: a bacterium, a protein and an atom would be a single point. A logarithmic ladder gives each factor of ten the same width, so each gets a rung of its own. That is a stance of this site: for things this small, a logarithmic axis is the only honest axis.
One more band on some ladders
Entries about swimming, or anything moving through a fluid, carry a shaded band, the syrup line: the position where, for the stated fluid, temperature and speed, a swimmer's Reynolds number — a ratio of inertia to stickiness — drops to 1 and viscosity starts to dominate. Its conditions are always written beside it, for example water at 20 °C and 30 µm/s, because changing the speed or the fluid moves it. How sizes are sourced is explained under How entries are checked.