# Microscopic Measurements

## tiny scales for tiny objects

© 2014 by KV5R. Rev. June 1, 2014.

### Introduction

In this article we’ll discover the basics and terminology of micro-measurements and micrometry. This background knowledge is essential for understanding microscopy and the subsequent articles in this series.

The first thing we need to understand is microscopic scales and measurements. We’re all familiar with measurements at visual scales, such as inches, feet, and miles; and/or centimeters, meters, and kilometers. Before discussing anything about microscopy, we need to become familiar with unusually small measurements (micrometry). Microscopy uses the metric system. Readers from other countries may skip the first part, but those from the U.S. that don’t work in a scientific field may wish to review.

### Metric System, Reviewed

• The metric system is a decimal system based on pure water and denominated by powers of 10.
• The base unit of length is the meter (m); the base unit of volume is the Liter (L), and the base unit of weight is the gram (g).
• There is a 1000:1 ratio of grams to Liters, so 1 Liter (of water) weighs 1 kilogram, and 1 milliLiter weighs 1 gram.
• There is a 1000:1 ratio of Liters to Meters, so 1000 Liters (of water) will occupy 1 cubic meter, and weigh 1000 kilograms (1 metric ton).
• 1 Liter (L) weighs 1 kilogram (2.2 pounds) and is 1000 cubic centimeters (cc); a 10cm (3.937″) cube.
• 1 deciLiter (dL) (= 0.1 Liter = 100mL or cc) weighs 100 grams; a ≈4.64 cm (≈1.8″) cube.
• 1 milliLiter (mL) (= 0.001L = 0.01 dL = 10-3L = 1cc) weighs 1 gram and is 1 cubic centimeter (cc).
• * When you read the letter μ, don’t say ‘u’ — say ‘micro.’ It is not the letter u, it is the Greek letter called ‘mu’ and, though frequently misspelled with a ‘u’, is properly represented in HTML with the sequence &mu; . It may also be inserted into most word processors by selecting Insert, Special Character from the menu thereof.
1 microLiter (μL*) (= 0.000 001L = 0.001mL = 10-6L) weighs 1 milligram (mg, 0.001 gram) and is 1 cubic millimeter (mm3).
• Further divisions by 1000: nano (billionth = 10-9m), pico (trillionth = 10-12m), femto (quadrillionth = 10-15m).

Of course, everything else besides water weighs something different, depending on its specific gravity (SG), and even water density changes a little with temperature.

#### Common Lengths in Microscopy

• millimeters (mm, 10-3m) — there are 25.4mm in 1 inch. Small visible bugs, such as gnats, are ≈1–3mm in length. If you have good eyes (or good glasses), the smallest bugs you can see (such as a chigger/mite) are about 0.5mm, which appear as a tiny dot without any visible detail.
• * Micrometer = micron, but micron was officially deprecated by the SI in 1967. Micrometer (the measure) is pronounced MY-kro-MEE-ter, not my-KROM-uh-ter, which, though spelled the same (in the US), refers to a machinist’s measuring tool. The pronunciation is disambiguated by the context. In other countries, they are disambiguated by spelling, where the measure is micrometre, and the tool is micrometer.
micrometers* (μm, 10-6m) — there are 1000μm in 1mm, thus, 1μm is 1/1000th of 1mm. The micrometer (μm) is the basic length unit in light microscopy (hence, the “micro” in microscope). Examples: a grain of sand or a mite is about 500μm; most multi-cellular pond critters are about 50–500μm; blood cells are about 10–20μm; and common bacteria are about 0.5–5μm. Visible light has a wavelength of about 0.4–0.7μm.
• nanometers (nm, 10-9m) — there are 1 thousand nm in 1μm, or 1 million nm in 1mm, or 1 billion nm in 1 meter. “Nanotechnology” generally refers to the manufacture of things smaller than 100nm (0.1μm); visible light waves are ≈400–700nm; and viruses are ≈20–300nm, which is why they can’t be seen with a light microscope.

#### Common Volumes in Microscopy

• Liter — Many common lab chemicals are sold by the liter.
• deciLiter — many chemical batch recipes exist that produce 1 deciLiter (100mL) of a reagent, stain, or solution. 100mL is just a traditional standard bulk quantity to make. That’s a little under 4 ounces, which, if you’re gonna buy a reasonably-priced quantity of sundry acids, chemical powders, mineral and metal compounds, organic solvents and such, you might as well just whip up a 100mL batch so your measurements don’t have to be so precise, and you end up with enough to last a good while. You might save some money by making 10mL batches of stuff, but you run out 10x more often, and the recipe measurements must be 10x more precise.
• milliLiter (mL) — used in microscopy to measure (and dilute) the various chemicals and stains. 1mL = 1cc, which is the volume of the smallest disposable medical syringe (typically an insulin syringe). Typical sizes for small plastic bottles are 10, 15, 30, 60, and 100mL. For the USA folks, there’s a bit under 30mL (29.57) in 1 US fluid ounce, ≈5mL per teaspoon, ≈15mL per tablespoon, and ≈237mL per kitchen “cup.” (8 US fl. oz.)
• drops — imprecise but frequently used, there are about 20–60 drops per mL, depending on the dropper and the liquid’s viscosity and surface tension. Drops should never be used as a measure in a chemical recipe (yet they are), but are better suited to protocols that call for adding something “drop-wise” (drop by drop) until something happens—a pH is reached, a color changes, etc.—as in titration. “Drops” are also frequently used in microscopy when adding some liquid to a slide, since most people don’t have expensive precision micro-pipettors, and such accuracy usually isn’t necessary.
• microLiter (μL) — typically used in cell counting, 1μL = 1 cubic millimeter.

### Practical Uses

When we buy lab glassware and lab plasticware; and chemical supplies and stains, they’re almost always in metric units. Then we make a variety of precise mixtures and dilutions, always in metric units. It’s important to remember the relationship between grams and milliliters because many recipes will call for mixing some grams of this and that into some milliliters of some liquid, usually water. For the most precise mixtures and dilutions, one should measure all components by weight, not volume. Digital gram and milligram scales are fairly inexpensive (≈\$20 each), costing less than a set of precision glass pipettes, graduated cylinders, and beakers. Thus, any recipe that calls for some milliliters of water may instead be weighed in grams.

Microscopic specimens are frequently identified by their measurements, being described by the typical length of their longest axis, though sometimes both long and short axes are given when necessary. Measuring microscopic objects is called “micrometry,” and is usually performed with a precision scale (called a reticle) in the eyepiece, or with a digital imager and the measurement features of its related software. In microscopy, we use measurements that are invisible, so it’s a little harder to imagine the relative sizes of specimens, yet a vastly diverse living world exists within that one millimeter, and their sizes vary by a 1000:1 ratio. Cells are measured in micrometers (μm), and some cells are much larger than animals with 1,000 or more cells. Hemacytometers measure area in square millimeters and volume in microLiters (mm3 or μL). A tiny drop of blood on the end of a fine needle is about 1 microLiter, and may contain 5 million red blood cells.

On a wet-mount, the height of the coverslip over a flat slide is determined by the amount of water under it. As the water evaporates around the edges of the slip, it lowers until it begins to mash the specimens therein, then the surface tension breaks and an area of air pops under the slip. While observing, it is important to occasionally add a drop of water to the edge of the slip to keep it floating 100-200μm or so above the slide, giving the larger critters some space to roam—but not too much! because when they move vertically it’s hard to keep them in the focal plane.

Fortunately, the more you work with it, the easier it gets, and you’ll soon become as familiar with micrometers as with inches or centimeters.

Next, we’ll take a brief look at microscope optics.

—KV5R