OCR Specification focus:
‘Use appropriate analogue apparatus to record measurements—length, temperature, pressure, force, angles, volume—and interpolate between scale markings accurately.’
Analogue measurement underpins experimental physics, requiring students to read and record data using traditional instruments. Mastery of interpolation ensures precise values are obtained from continuous analogue scales.
Understanding Analogue Measurements
Analogue measurements involve observing physical quantities using graduated scales rather than digital displays. Examples include thermometers, rulers, micrometers, vernier calipers, and pressure gauges. These devices convert a continuous physical variable—such as length or pressure—into a directly readable scale.
Analogue Measurement: A measurement obtained using a continuous scale rather than discrete digital values, where precision depends on the observer’s interpretation of the scale markings.
Analogue instruments remain vital because they allow students to develop manual precision and awareness of measurement limitations, including human reading error and parallax error.
Importance in Physics Experiments
In OCR A-Level Physics, students must demonstrate competence in using analogue instruments for:
Measuring length, e.g., with rulers or vernier calipers.
Measuring temperature, e.g., with mercury or alcohol thermometers.
Measuring pressure, e.g., with Bourdon gauges or manometers.
Measuring force, e.g., with spring balances or Newton meters.
Measuring angles, e.g., with protractors or angular scales.
Measuring volume, e.g., with burettes or measuring cylinders.
Each instrument requires careful alignment, accurate eye positioning, and awareness of the instrument’s least count—the smallest measurable increment.
Reading Analogue Scales Accurately
Scale Markings and Least Count
The least count determines the precision of an instrument. It represents the smallest division between scale markings.
Least Count: The smallest measurable increment on an instrument’s scale that determines the minimum resolution of measurement.
For instance, a standard metre ruler with millimetre divisions has a least count of 1 mm, while a vernier caliper can measure to 0.1 mm or finer.
Always record readings to one decimal place beyond the smallest scale division, estimated using interpolation.
Parallax Error and Correct Eye Position
Parallax error arises when the observer’s line of sight is not perpendicular to the scale. To minimise this:
Align the eye directly above the measurement mark.
Avoid angled viewpoints.
Use mirrors or fiducial marks where available.
Parallax Error: Apparent displacement of a scale reading due to an incorrect viewing angle, leading to systematic measurement error.
Ensuring the correct viewing angle is a fundamental experimental skill expected in all OCR practical assessments.
Interpolation Between Scale Markings
Interpolation enables students to estimate values between two adjacent scale marks for improved accuracy. This technique bridges the gap between visible markings and real continuous values.
When interpolating:
Identify the two nearest scale divisions between which the pointer or meniscus lies.
Visually divide the interval into ten equal parts.
Estimate the fractional value according to the pointer’s position.
Record the reading with an extra significant figure to reflect interpolation.
For example, a thermometer mark lying halfway between 24°C and 25°C should be recorded as 24.5°C.
Interpolation enhances measurement resolution beyond the instrument’s least count and aligns with OCR’s requirement to “interpolate between scale markings accurately.”
Common Analogue Instruments and Techniques
Length Measurement
Rulers measure large distances with limited precision. For higher accuracy:
Place the ruler in contact with the object.
Avoid zero error by ensuring the scale starts at the true zero point.
Vernier Calipers provide readings to tenths or hundredths of a millimetre.
Labeled vernier caliper showing outside/inside jaws, depth probe, and both main and vernier scales. The diagram illustrates how the secondary vernier scale enables interpolation between main-scale markings. Use it to discuss least count and recording an extra significant figure. Source.
Vernier Scale: A secondary sliding scale on a measuring instrument that allows readings to a fraction of the smallest main scale division.
Micrometers are used for extremely small dimensions, such as wire diameters, with screw-driven spindles for fine control.
Labeled micrometer showing anvil, spindle, ratchet stop, sleeve (0.5 mm resolution), thimble (0.01 mm resolution), and lock. The figure clarifies how rotation of the thimble advances the spindle to resolve hundredths of a millimetre. It neatly illustrates where readings are taken to achieve fine interpolation. Source.
Temperature Measurement
Analogue liquid-in-glass thermometers rely on volume expansion of a liquid. When reading them:
Keep the thermometer vertical.
Align eye level with the top of the liquid column.
Avoid touching the bulb during measurement to prevent heat transfer.
Pressure and Force Measurement
Analogue pressure gauges often employ elastic deformation or fluid columns. Spring balances operate via Hooke’s law.
EQUATION
—-----------------------------------------------------------------
Hooke’s Law (F) = k × x
F = Force (N)
k = Spring constant (N/m)
x = Extension (m)
—-----------------------------------------------------------------
Hooke’s law underpins the operation of spring balances, connecting mechanical deflection to measurable force.
Measuring Angles
When using a protractor or angular scale:
Ensure the centre point is aligned with the vertex.
Read the inner or outer scale correctly depending on orientation.
Estimate to the nearest half-degree through interpolation.
Measuring Volume
Instruments such as burettes, pipettes, and measuring cylinders rely on meniscus readings.
To read correctly:
Position the eye level with the bottom of the meniscus.
Read the scale to the nearest 0.1 mL using interpolation.
These techniques are central to precise volumetric measurements in experimental physics and chemistry.
Recording and Reporting Analogue Data
When documenting analogue measurements:
Always include units in every recorded value.
Record uncertainties, typically half the least count or the estimated reading error.
Use consistent significant figures across related readings.
Represent results in a table or graph with clear labelling.
Uncertainty: An estimate of the possible error in a measurement, expressing the range within which the true value is likely to lie.
Interpolated analogue readings often carry smaller random uncertainties but may include systematic errors from calibration or user bias.
Improving Reliability in Analogue Measurements
To enhance reliability and reproducibility:
Take repeat readings and calculate a mean value.
Use fiducial markers (fixed reference points) for timing or alignment.
Calibrate instruments before use.
Note ambient conditions (temperature, pressure) that might influence the instrument.
Combining careful reading, interpolation, and awareness of uncertainties ensures analogue measurements meet the precision required in OCR A-Level Physics practical assessments.
FAQ
Accuracy refers to how close a measured value is to the true value. Precision is the consistency of repeated readings, regardless of their correctness. Resolution is the smallest detectable change an instrument can measure — often linked to the least count.
A measurement can be precise but inaccurate if a systematic error (like zero error) is present. High-resolution instruments improve precision but do not guarantee accuracy without proper calibration.
Interpolation assumes the observer can visually divide scale intervals accurately. With coarse scales (large divisions), this becomes harder because:
The spacing between marks is too large for meaningful estimation.
Parallax and eye misjudgement cause larger fractional errors.
Instruments with finer divisions or vernier attachments enable more reliable interpolation by allowing smaller fractional readings.
Thermal expansion alters the physical dimensions of measuring devices and the objects measured. For example:
A steel ruler may expand, making lengths appear shorter.
Liquids in thermometers expand non-linearly at extreme temperatures.
To minimise these effects:
Take measurements at room temperature.
Allow instruments to stabilise thermally before use.
Apply temperature correction factors if available.
Mirrors help reduce parallax error. When viewing the pointer, the observer aligns their eye so the pointer covers its reflection in the mirror.
This ensures the line of sight is perpendicular to the scale, preventing over- or underestimation of the true reading. Such mirrors are common in analogue meters and ammeters where precision is essential.
Zero error occurs when an instrument’s reading is not zero when the measured quantity is zero. It introduces a constant offset in all measurements.
Types include:
Positive zero error: Scale starts above zero — subtract the offset.
Negative zero error: Scale starts below zero — add the offset.
To correct it:
Check the instrument’s zero before each use.
Record the zero offset and adjust subsequent readings accordingly.
Practice Questions
Question 1 (2 marks)
A student uses a ruler with millimetre markings to measure the diameter of a metal rod. The student records a value of 12.6 mm.
(a) Explain how the student could justify recording a measurement to one decimal place beyond the smallest scale division.
(2 marks)
Mark Scheme for Question 1
1 mark: States that the student is estimating a value between two adjacent millimetre marks.
1 mark: Explains that interpolation allows a fractional reading beyond the smallest scale division to improve accuracy.
Question 2 (5 marks)
A student uses a vernier caliper to measure the thickness of a glass plate. The main scale reading is 3.5 mm and the vernier scale reading corresponds to the 7th division aligning with the main scale. Each vernier division equals 0.01 mm.
(a) Determine the total thickness of the glass plate.
(b) Explain how the use of the vernier caliper improves accuracy compared with using a standard ruler.
(c) Identify two possible sources of error and suggest how each could be minimised.
(5 marks)
Mark Scheme for Question 2
(a) Calculation (2 marks)
1 mark: Correctly identifies that total thickness = main scale + vernier reading.
1 mark: Substitutes values to obtain 3.57 mm.
(b) Explanation of accuracy improvement (1 mark)
1 mark: States that the vernier scale allows interpolation to 0.01 mm, giving higher precision than a standard ruler’s 1 mm divisions.
(c) Errors and minimisation (2 marks)
1 mark: Identifies parallax error; minimised by viewing the scale perpendicularly.
1 mark: Identifies zero error; minimised by checking and adjusting the zero alignment before taking readings.
