Magnification, Resolution and Calculations

This lesson develops the quantitative skills required by OCR module 2.1.1 (c). You must be able to calculate magnifications from photomicrographs, convert between units of length, use an eyepiece graticule and stage micrometer to measure specimens, and distinguish magnification from resolution. Calculations are a frequent source of marks in Paper 1 and Paper 3.

Key Equation: $\text{magnification} = \dfrac{\text{size of image}}{\text{size of actual (real) object}}$magnification=size of actual (real) objectsize of image​ This can be rearranged as: $\text{actual size} = \dfrac{\text{image size}}{\text{magnification}}$actual size=magnificationimage size​

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Units of Length

A-Level biology calculations demand fluency with SI prefixes. You must be able to convert rapidly between them.

Unit	Symbol	Equivalent in metres	Equivalent in mm
Metre	m	1 m	1,000 mm
Millimetre	mm	10⁻³ m	1 mm
Micrometre	µm	10⁻⁶ m	10⁻³ mm (0.001 mm)
Nanometre	nm	10⁻⁹ m	10⁻⁶ mm

Conversion Rules

• 1 mm = 1,000 µm = 1,000,000 nm
• 1 µm = 1,000 nm
• To convert mm → µm, multiply by 1,000.
• To convert µm → nm, multiply by 1,000.
• To convert nm → µm, divide by 1,000.
• To convert µm → mm, divide by 1,000.

Exam Tip: Before any magnification calculation, convert both measurements to the same unit. If your image measurement is in mm and your actual size in µm, you must convert one of them. Failure to do so is the most common mistake in calculation questions.

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The Magnification Equation

The core equation is:

$M = \dfrac{I}{A}$M=AI​

where:

• $M$M = magnification (no units, just "×number").
• $I$I = size of the image on the page.
• $A$A = actual size of the specimen.

A useful mnemonic is the triangle:

     I
   -----
   A | M

Cover $I$I to get $A × M$A×M, cover $A$A to get $I / M$I/M, cover $M$M to get $I / A$I/A.

Worked Example 1

A photomicrograph of a plant cell shows the cell as 85 mm wide. The scale bar, representing 20 µm, measures 4 mm on the image. Calculate (a) the magnification of the image and (b) the actual width of the cell.

(a) Magnification from the scale bar:

$M = \dfrac{I}{A} = \dfrac{4 \text{ mm}}{20 \text{ µm}} = \dfrac{4000 \text{ µm}}{20 \text{ µm}} = 200$M=AI​=20 µm4 mm​=20 µm4000 µm​=200

So the magnification is ×200.

(b) Actual width of the cell:

$A = \dfrac{I}{M} = \dfrac{85 \text{ mm}}{200} = 0.425 \text{ mm} = 425 \text{ µm}$A=MI​=20085 mm​=0.425 mm=425 µm

Worked Example 2

An electron micrograph of a mitochondrion shows it as 60 mm long at a magnification of ×30,000. Calculate the actual length of the mitochondrion in µm.

$A = \dfrac{I}{M} = \dfrac{60 \text{ mm}}{30{,}000} = 0.002 \text{ mm} = 2 \text{ µm}$A=MI​=30,00060 mm​=0.002 mm=2 µm

This is a typical mitochondrial length, confirming the answer is realistic.

Worked Example 3 (Rearranged)

A ribosome has an actual diameter of 25 nm. In an electron micrograph taken at ×500,000, how large will the ribosome appear?

$I = A \times M = 25 \text{ nm} \times 500{,}000 = 12{,}500{,}000 \text{ nm} = 12.5 \text{ mm}$I=A×M=25 nm×500,000=12,500,000 nm=12.5 mm

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Magnification vs Resolution

These two concepts must be kept distinct in your mind.

• Magnification is how much bigger the image is compared to the real object. It can be increased by adding more lenses or zooming digitally.
• Resolution is the smallest distance between two points that can still be distinguished as separate. It is limited by the wavelength of the illuminating radiation.

Beyond the resolution limit, further magnification produces no new detail — this is empty magnification. The image simply becomes blurrier.

Instrument	Typical max magnification	Resolution limit
Light microscope	×1,500	200 nm
TEM	×500,000	0.2 nm
SEM	×200,000	3–10 nm