calculate magnifications of images and actual sizes of specimens from drawings, photomicrographs and electron micrographs (scanning and transmission)

The Microscope in Cell Studies

Learning Objective

Calculate the magnification of images and determine the actual size of specimens from drawings, photomicrographs and electron‑micrographs (scanning and transmission).

1. Making Temporary Preparations (AO 1.1.1)

• Materials: clean glass slide, cover slip, distilled water or mounting medium, specimen (e.g., onion epidermis, cheek cells), staining solution (e.g., iodine, methylene blue), tweezers, fine needle, pipette, blotting paper.
• Procedure (check‑list with rationale):

  1. Place a small drop of water (or mounting medium) on the centre of a clean slide – the drop spreads the specimen evenly and prevents air bubbles.
  2. Transfer a thin fragment of the specimen onto the drop using tweezers or a needle – a thin fragment gives a clear image and reduces overlapping cells.
  3. If required, add a drop of stain; let it act for 10–30 s, then rinse gently with water – staining enhances contrast of internal structures.
  4. Blot excess liquid with blotting paper – removing surplus liquid avoids crushing the sample and reduces movement.
  5. Lower a cover slip at an angle and slide it down gently – this technique minimises trapped air bubbles that distort the image.
  6. Label the slide (specimen, stain, objective to be used, intended magnification) – essential for record‑keeping and for exam questions.
  7. Observe under the light microscope immediately; discard after use – temporary mounts are not suitable for long‑term storage.

• Safety notes: handle glassware with care, avoid direct eye exposure to bright light, wear gloves when using stains, dispose of stained material according to school policy.

2. Drawing Cells from Slides and Photomicrographs (AO 1.1.2)

• Choose a reference structure – select an organelle whose real size is known (e.g., nucleus ≈ 10 µm, chloroplast ≈ 5 µm).
• Maintain proportional scaling – use a ruler or a transparent grid on the screen to keep all parts in the same scale.
• Label clearly – name each organelle, indicate the scale bar (e.g., “1 mm = 20 µm”), and note the microscope settings (objective and eyepiece powers).
• Practice exercise – given a photomicrograph of an onion epidermal cell, students must:

  1. Measure the nucleus on the screen (or printed image).
  2. Calculate its actual size using the scale bar.
  3. Reproduce the cell at the same scale on paper.

3. Types of Microscopes Used in Cell Biology

4. Key Concepts

4.1 Magnification (AO 1.1.5)

The ratio of the size of the image to the size of the actual specimen.

For an optical microscope the total magnification (M) is the product of the objective power (m_o) and the eyepiece power (m_e).

\$\$

M = m{o}\times m{e}

\$\$

Remember: keep the number of significant figures consistent with the least‑precise measurement (usually 2 sf for microscope powers).

4.2 Resolution (AO 1.1.5)

The minimum distance between two points that can be distinguished as separate.

Resolution is limited by the wavelength of illumination and the numerical aperture (NA) of the objective. For light microscopes the Rayleigh criterion gives a practical limit of about 0.2 µm:

\$\$

d = \frac{0.61\lambda}{\text{NA}} \;\;\approx\;0.2\;\mu\text{m (visible light, NA≈1.4)}

\$\$

Magnification alone cannot reveal detail smaller than the resolution limit.

5. Calculating Magnification (AO 1.1.3)

• If the objective and eyepiece powers are known: M = m_o × m_e.
• If only a scale bar is given, first determine the pixel‑to‑real conversion factor (see §6) and then use the image length in pixels.

6. Determining the Actual Size of a Specimen (AO 1.1.3)

6.1 General Formula

When the image dimension (I) and total magnification (M) are known:

\$\$

S = \frac{I}{M}

\$\$

S = real size (same units as I).

6.2 Using Pixels – Photomicrographs, SEM & TEM

1. Measure the length of the scale bar on the screen or printed image (in pixels) → L_px.
2. Note the real length that the scale bar represents (L_real, e.g., 2 µm or 100 nm).
3. Calculate the conversion factor:

   \$k = \frac{L{real}}{L{px}}\quad(\text{µm / px or nm / px})\$

4. Measure the feature of interest in pixels (I_px).
5. Actual size:

   \$S = I_{px}\times k\$

6.3 Hand‑drawn Sketches

1. Measure the feature on the paper with a ruler → I_draw (mm).
2. Know the total magnification used for the sketch (usually written on the diagram). If missing, calculate M from a reference structure.
3. Apply S = I_draw/M. Convert the result to µm (1 mm = 1000 µm) and keep appropriate significant figures.

7. Using an Eyepiece Graticule & Stage Micrometer (AO 1.1.4)

1. Calibrate the graticule:

   • Place a stage micrometer (e.g., 0.01 mm divisions) on the stage.
   • Focus with the objective you will use for observations.
   • Count how many graticule divisions span a known length on the micrometer.
   • Calculate the value of one graticule division:

     \$\text{Division value} = \frac{\text{Known length (µm)}}{\text{Number of divisions}}\$

2. Apply to a specimen:

   • Count the graticule divisions that cover the structure of interest.
   • Multiply by the division value to obtain the real size.

3. Worked example:

   • Stage micrometer: 100 µm = 10 mm.
   • With a 40× objective and 10× eyepiece, 1 graticule division spans 5 µm.
   • A nucleus measures 6 divisions → real size = 6 × 5 µm = 30 µm.

8. Worked Examples

Example 1 – Hand‑drawn Light‑Microscope Sketch

Sketch measurement: nucleus = 12 mm. Sketch made at 400× total magnification.

\$\$

S = \frac{12\ \text{mm}}{400}=0.030\ \text{mm}=30\ \mu\text{m}

\$\$

Example 2 – Photomicrograph of a Bacterial Cell

• Scale bar: 2 µm = 150 px
• Measured bacterial length: 450 px

\$k = \frac{2\ \mu\text{m}}{150\ \text{px}} = 0.0133\ \mu\text{m/px}\$

\$S = 450\ \text{px}\times0.0133\ \mu\text{m/px}=6.0\ \mu\text{m}\$

Example 3 – SEM of a Pollen Grain

\$k = \frac{10\ \mu\text{m}}{200\ \text{px}} = 0.05\ \mu\text{m/px}\$

\$S = 800\ \text{px}\times0.05\ \mu\text{m/px}=40\ \mu\text{m}\$

Example 4 – TEM of a Mitochondrion

• Scale bar: 100 nm = 250 px
• Measured crista width: 120 px

\$k = \frac{100\ \text{nm}}{250\ \text{px}} = 0.40\ \text{nm/px}\$

\$S = 120\ \text{px}\times0.40\ \text{nm/px}=48\ \text{nm}\$

Example 5 – Using an Eyepiece Graticule

Stage micrometer: 0.01 mm (10 µm) divisions. With a 40× objective and 10× eyepiece, 1 graticule division = 5 µm.

A chloroplast spans 8 graticule divisions.

\$S = 8 \times 5\ \mu\text{m}=40\ \mu\text{m}\$

9. Quick‑Reference Tables

9.1 Formulas (linked to syllabus outcomes)

9.2 Light Microscope vs. SEM vs. TEM (AO 1.1.5)

10. Flowchart – From Image to Real Size