Lab measurements & scale

Turn what you see in a microscope into numbers.

The idea

Magnification is image size divided by actual size (rearranged: image = actual × magnification), and it only works when both sizes are in the same unit — 1 mm = 1,000 µm and 1 µm = 1,000 nm. A light microscope’s total magnification is eyepiece × objective (10× × 40× = 400×), but its resolution is limited to about 200 nm, which is why ribosomes and membranes need an electron microscope. A scale bar is a line drawn on an image that represents a stated real length; its drawn length is that real length times the magnification, and unlike a printed "×400" it stays correct when the image is resized. For solutions, C₁V₁ = C₂V₂ says the amount of solute is conserved when you dilute, so you can find the volume of stock needed for any target concentration; whatever you calculate, round to the significant figures your instrument can actually justify.

Work through an example

A drawing of a cheek cell measures 30 mm across, and the real cell is 60 µm wide. Convert first: 30 mm = 30,000 µm, so magnification = 30,000 / 60 = 500×. To add a scale bar representing 20 µm, draw it 20 × 500 = 10,000 µm = 10 mm long. In the same lab, to make 50 mL of 0.2 M sucrose from a 1.0 M stock: V₁ = C₂V₂ / C₁ = 0.2 × 50 / 1.0 = 10 mL of stock, made up to 50 mL with 40 mL of water.

What to watch for

Dividing 30 mm by 60 µm without converting gives 0.5 — a nonsense answer that would mean the drawing is smaller than the cell. Always convert both measurements to the same unit before dividing. And a calculator’s 500.00× does not mean you measured that precisely: a ruler reads to the nearest millimeter, so 500× (two significant figures) is the honest answer.