use an eyepiece graticule and stage micrometer scale to make measurements and use the appropriate units, millimetre (mm), micrometre (µm) and nanometre (nm)

Microscope Measurements in Cell Studies (Cambridge 9700)

Learning Objectives (AO1‑AO3)

• AO1 – Knowledge & Understanding: Identify microscope parts, describe safety, prepare temporary slides, draw cells to scale, and state the relationship between magnification, resolution and numerical aperture (NA).
• AO2 – Application of Knowledge: Calibrate an eyepiece graticule with a stage micrometer, calculate total magnification, convert between mm, µm and nm, and record measurements with correct significant figures.
• AO3 – Evaluation: Analyse sources of error (parallax, focus, calibration drift, depth of field, counting), estimate their magnitude and suggest improvements.

1. Safety & Handling of the Light Microscope (AO1)

• Never look directly at a bright light source – use the diaphragm or a diffuser.
• Handle slides by the edges; avoid touching the glass surfaces.
• Clean objective and ocular lenses with lint‑free lens paper only.
• Keep the microscope covered when not in use to prevent dust accumulation.
• Turn the coarse focus knob only with the low‑power (4× or 10×) objective in place.
• Never force the rotating nosepiece; if it sticks, turn it gently back and forth.

2. Preparing a Temporary Slide (Quick‑Check) (AO1)

1. Place a clean glass slide on the stage.
2. Put a drop of water (or a suitable stain such as iodine, methylene blue, etc.) on the specimen.
3. Lower a cover‑slip at an angle to spread the liquid and avoid air bubbles.
4. If the slide will be examined for more than a few minutes, seal the edges with a tiny amount of glycerol or water.
5. Label the slide (e.g., “Onion epidermis – water”) and note the preparation method in your notebook.

3. Key Components of a Light Microscope (AO1)

4. Numerical Aperture, Magnification and Resolution (AO1‑AO2)

• Magnification – total magnification = objective × eyepiece.
• Numerical Aperture (NA) – a measure of the light‑gathering ability of an objective:

  
  NA = n sin θ (where *n* is the refractive index of the medium between specimen and objective, *θ* is the half‑angle of the cone of light).

• Resolution (minimum resolvable distance) – given by Abbe’s equation:

  
  d ≈ 0.61 λ / NA (λ = wavelength of light, typically 550 nm for green light).

• Practical rule‑of‑thumb: maximum useful magnification ≈ 1000 × NA. Beyond this you obtain “empty magnification” – the image looks larger but no extra detail is revealed.
• Typical theoretical limits (λ ≈ 550 nm):

  • 4× objective (NA ≈ 0.10) → d ≈ 3.4 µm
  • 10× objective (NA ≈ 0.25) → d ≈ 1.3 µm
  • 40× objective (NA ≈ 0.65) → d ≈ 0.5 µm
  • 100× oil (NA ≈ 1.30) → d ≈ 0.26 µm

Resolution vs. Magnification Summary Table

5. Calibration of the Eyepiece Graticule (AO2)

5.1 Procedure (for each objective)

1. Place the stage micrometer on the stage and secure it with the stage clips.
2. Start with the lowest‑power objective (e.g., 4×) and bring the micrometer scale into sharp focus using the coarse then fine focus knobs.
3. Rotate the nosepiece to the objective you wish to calibrate (e.g., 40×).
4. Refocus if necessary – the divisions must be crisp.
5. Look through the eyepiece and align the graticule divisions with the micrometer divisions.
6. Count how many graticule divisions span a known length on the micrometer (commonly 10 µm or 100 µm).
7. Calculate the size of one graticule division:

   
   Size of one division (µm) = Known length (µm) ÷ Number of graticule divisions counted

8. Record the result in the calibration table (see 5.2).
9. Repeat for every objective you will use.

5.2 Sample Calibration Table

6. Units, Conversions & Significant Figures (AO2)

Tip (AO2): Keep the same number of significant figures throughout a calculation. If the calibration gives 0.40 µm per division (two s.f.), final results should be reported to two s.f. (e.g., 48 µm, not 48.0 µm).

7. Example Calculations (AO2)

7.1 Size of One Graticule Division (40× objective)

Counted 25 divisions across a 10 µm segment of the stage micrometer.

One division = 10 µm ÷ 25 = 0.40 µm

7.2 Measuring a Plant Cell

Cell spans 120 graticule divisions under the same objective.

Cell size = 120 × 0.40 µm = 48 µm

• 48 µm = 0.048 mm
• 48 µm = 48 000 nm

7.3 Determining Total Magnification

Objective = 40×, Eyepiece = 10× → Total magnification = 40 × 10 = 400×.

7.4 Photomicrograph Exercise (AO1‑AO2)

Students are given a photomicrograph of an onion epidermal cell with a scale bar labelled “10 µm”. The image was taken with a 40× objective and a 10× eyepiece.

1. Read the scale bar: 1 cm on the printed image = 10 µm actual.
2. Measure the length of the cell on the printed image (e.g., 6.0 cm).
3. Calculate the actual length:

   
   Actual length = (Measured length ÷ Scale‑bar length) × 10 µm

   = (6.0 cm ÷ 1 cm) × 10 µm = 60 µm

4. Confirm the result using the calibrated graticule (25 divisions = 10 µm → 1 division = 0.40 µm; 60 µm ÷ 0.40 µm ≈ 150 divisions).

8. Sketching Cells to Scale (AO1‑AO3)

1. Measure the length and width of the cell in graticule divisions.
2. Convert the division count to µm using the calibration table.
3. Choose a drawing scale (e.g., 1 mm on paper = 10 µm actual).
4. Draw the cell on graph paper, label key structures (cell wall, nucleus, vacuole) and add a calibrated scale bar.
5. Record the drawing’s magnification and the calibration data used.

Activity – Sketch from a Photomicrograph

Using the photomicrograph from 7.4, students should:

• Sketch the cell at the chosen drawing scale.
• Indicate the total magnification (400×) on the sketch.
• Include a scale bar (e.g., 5 mm = 50 µm).
• Write a brief evaluation of any uncertainties (e.g., difficulty reading the scale bar, parallax).

9. Sources of Error & Quantitative Estimation (AO3)

• Parallax error – reading the graticule from an angle gives a systematic offset.

  
  Mitigation: keep the dominant eye centred on the eyepiece tube and keep the head still.

• Focus error – an out‑of‑focus micrometer scale leads to mis‑counted divisions.

  
  Mitigation: use fine focus until the micrometer lines are razor‑sharp.

• Calibration drift – temperature changes can expand the stage micrometer.

  
  Typical impact: ±0.02 µm for a 10 °C change.

• Depth of field – thick specimens may have only part of the structure in focus, causing under‑estimation of size.

  
  Mitigation: adjust the condenser and use fine focus to bring the whole structure into view; note the limitation in the report.

• Counting error – difficulty reading partial divisions.

  
  Rule of thumb: estimate to the nearest 0.1 division; this adds an uncertainty of ±0.04 µm when one division = 0.40 µm.

Overall estimated uncertainty (example for 40× objective): ±0.5 µm (≈ ±1 % of a 48 µm measurement). Students should state the dominant source(s) and suggest how the uncertainty could be reduced.

10. Practical Tips Linked to Assessment Objectives

• Record calibration for each objective – essential for AO2 (organise information).
• Use the same dominant eye for all measurements – reduces systematic parallax error (AO3).
• Include a calibrated scale bar on every sketch – meets AO1 (present information accurately).
• State sources of error, estimate their magnitude and suggest improvements – directly addresses AO3.
• Keep a neat data table with units and significant figures – AO2.

11. Summary Checklist (AO1‑AO3)

1. Prepare a clean temporary slide (water or appropriate stain).
2. Calibrate the eyepiece graticule for each objective; fill in the calibration table.
3. Calculate total magnification (objective × eyepiece).
4. Measure specimens by counting graticule divisions; convert to µm, then to mm or nm as required.
5. Draw the specimen to scale, adding a calibrated scale bar.
6. Identify possible errors (parallax, focus, calibration drift, depth of field, counting) and give a quantitative estimate.
7. Record all data neatly, using the correct number of significant figures.

12. Further Reading (Optional A‑Level Extension) (AO1)

• Resolution limits of light microscopy vs. electron microscopy (TEM < 1 nm).
• Effect of numerical aperture on resolution – detailed derivation of d ≈ 0.61 λ / NA.
• Fluorescence microscopy – how specific staining improves contrast without compromising measurement accuracy.
• Advanced image analysis software for automated measurement and error propagation.