Convert measurements between millimetres (mm) and micrometres (μm).

2.2 Size of Specimens

Learning Objectives

• Recall and use the relationship 1 mm = 1000 µm.
• Convert measurements accurately between mm and µm.
• State and apply the magnification formula M = image size ÷ actual size.
• Re‑arrange the magnification formula to find any missing quantity.
• Appreciate the practical relevance of these conversions in microscopy and biology.

Key Concepts

• 1 mm = 10⁻³ m
• 1 µm = 10⁻⁶ m
• Therefore 1 mm = 1000 µm and 1 µm = 0.001 mm.

Conversion Formulae

From mm to µm

From µm to mm

Magnification Formula

When a specimen is viewed under a microscope (or any enlarging instrument):

Both quantities must be expressed in the same units (either mm or µm). If they are not, convert one of them using the factor above.

Re‑arranging the formula

• Actual size = image size ÷ M
• Image size = M × actual size

Example: A microscope gives a magnification of 250× and the actual cell is 8 µm long. Image size = 250 × 8 µm = 2000 µm = 2 mm.

Practical Relevance

• Microscope calibration bars are often marked in mm; converting to µm lets you compare with textbook cell sizes.
• Biologists routinely switch between mm (tissues, organs) and µm (cells, organelles) when recording measurements.
• Accurate conversion is essential for calculating magnification, field of view, and for reporting results in exams.

Typical Sizes of Biological Specimens

Worked Examples

1. Convert 0.25 mm to µm.
   0.25 mm × 1000 = 250 µm
2. Convert 750 µm to mm.
   750 µm ÷ 1000 = 0.75 mm
3. A microscope slide shows a leaf vein 2 mm long. Express this length in µm.
   2 mm × 1000 = 2000 µm
4. Calculate the magnification if a cell 8 µm long appears 2 mm on the screen.
   Convert image size: 2 mm × 1000 = 2000 µm.
   M = 2000 µm ÷ 8 µm = 250×
5. Find the actual size of a bacterium that appears 1.5 mm long at a magnification of 300×.
   Actual size = image size ÷ M = 1.5 mm ÷ 300 = 0.005 mm = 5 µm.
6. Determine the image size of a 0.12 mm (120 µm) cell when viewed at 8× magnification.
   Image size = M × actual size = 8 × 0.12 mm = 0.96 mm (or 8 × 120 µm = 960 µm).

Practice Questions

1. Convert 0.008 mm to µm.
2. What is 1200 µm in mm?
3. A pollen grain measures 30 µm in diameter. Write its diameter in mm.
4. If a bacterial cell is 2 µm long, how many such cells could be placed end‑to‑end in a 1 mm line?
5. Fill in the table:
     a) 0.5 mm = ___ µm   b) 250 µm = ___ mm
6. A specimen 0.12 mm long appears as a 0.96 mm image under a microscope. Determine the magnification.
7. Given a magnification of 150× and an image size of 3 mm, find the actual size of the specimen (express in µm).
8. Re‑arrange the magnification formula to find the magnification when the actual size is 0.004 mm and the image size is 0.8 mm.

Answers to Practice Questions

1. 0.008 mm × 1000 = 8 µm
2. 1200 µm ÷ 1000 = 1.2 mm
3. 30 µm ÷ 1000 = 0.03 mm
4. 1 mm = 1000 µm → 1000 µm ÷ 2 µm = 500 cells
5. a) 0.5 mm × 1000 = 500 µm
     b) 250 µm ÷ 1000 = 0.25 mm
6. Image size = 0.96 mm = 960 µm; actual size = 0.12 mm = 120 µm
   M = 960 µm ÷ 120 µm = 8×
7. Actual size = image size ÷ M = 3 mm ÷ 150 = 0.02 mm = 20 µm
8. M = image size ÷ actual size = 0.8 mm ÷ 0.004 mm = 200×