Cell structure: (e) the use and manipulation of the magnification formula

The idea

You must be able to use and rearrange the magnification relationship: magnification = image size ÷ actual size. Learn to identify which two quantities are given and which is required, then rearrange before substituting. If magnification and actual size are known, image size = magnification × actual size. If image size and magnification are known, actual size = image size ÷ magnification. Keep units consistent: convert micrometres to millimetres (1 mm = 1000 µm) or to metres (1 m = 10⁶ µm) before calculating, and state the unit in the answer. For example, a structure 20 µm across drawn at ×500 has an image size of 500 × 20 µm = 10 000 µm = 10 mm. Worked in reverse, an image of 8 mm at ×400 represents an actual size of 8 mm ÷ 400 = 0.02 mm = 20 µm. Always sanity-check that the answer is plausible for a cell or organelle.

What earns the marks

• Correctly states the relationship magnification = image size ÷ actual size.
• Rearranges the formula correctly to find image size or actual size as required.
• Substitutes values with consistent units, converting between µm, mm and m accurately.
• Gives the final answer with an appropriate unit and a sensible magnitude for a cell or organelle.
• Shows the rearrangement or working so the method can be followed.

Common mistakes and how to put them right

• Multiplying when division is needed, or vice versa.

  Put it right: Is to rearrange the formula explicitly before substituting.

• Mixing micrometres and millimetres without converting.

  Put it right: Is to convert all lengths to the same unit first.

• Reporting an answer with no unit or an implausible magnitude.

  Put it right: Is to attach the unit and check the size against a typical cell.

Exam tips

• Write the rearranged formula down before inserting numbers.
• Convert every length to the same unit, then convert the answer back if needed.
• Check the magnitude: a whole cell is typically tens of micrometres across.