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Measuring and Counting with a Light Microscope

Author(s): David R. Caprette, PhD

Resolving and Reporting Dimensions

Suppose that at a total magnification of 400x, each division of an ocular scale is determined to be 2.5 µm wide. Suppose you then use the scale to estimate the length of a flagellum of an individual Chlamydomonas reinhardi. Let us further suppose that after superimposing a line over the apparent origin of the flagellum, the end appears to reach 4.5 divisions from the beginning. The calculated length, then, comes out to 4.5 x 2.5 = 11.25 µm. Is that the length that you should report?

The quantity, 11.25 µm, implies an accuracy to the nearest hundredth of a micrometer. One hundredth of a micrometer is just 10 nanometers, or 10 billionths of a meter.  Ten nanometers is the diameter of some molecules, or even atoms. Obviously, you cannot resolve molecules with the aid of a light microscope. In fact, it takes very high magnifications to image a molecule in an electron microscope, which provides far greater resolution than a light microscope.

The calibration, 2.5 µm per division, doesn't mean each division is accurate to half a micrometer. It only means that we use that calibration as a multiplier. A final result should be reported with an accuracy that reflects the precision of the instrument. The very best resolution we might expect at 400x is to the nearest 1 µm, and then only under ideal conditions. The length of this flagellum should be reported as 11 µm.

Suppose now that you intend to measure diameters of a couple of dozen filaments or so, in order to report a mean value. You would record the length with full precision, which in this case is 11.25 µm. After collecting the raw data and determining mean diameter you then suppress excess digits. For example, suppose you collect data from 23 cells and obtain a mean value of 11.9022 µm. The mean should be reported as 12 µm. You must not report the mean as 12.0 µm, which implies an accuracy to the nearest tenth of a micrometer.