The Mirror That Would Not Give 15 cm
In a Class 9 physics class of 40 in a rural school in Idukki, the teacher demonstrates the focal length of a concave mirror. The school has one mirror, one metre scale and a candle; the mirror's actual focal length is about 15 cm. Groups measure the image distance when the image is sharply focused on a screen. Six of eight groups report values between 21 and 24 cm. The teacher writes the textbook value 15 cm on the board and tells the class the groups 'measured carelessly'. One student, Anu, asks why her group's value was consistently 23 cm and is told not to argue. The same practical must be repeated for the Class 10 batch next week, and the syllabus is behind schedule.
1. Identify the likely sources of error and judge whether the teacher's explanation is adequate.
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The teacher's explanation is not adequate. Six of eight groups clustering at 21–24 cm is not random carelessness; it suggests a systematic error shared by the apparatus or the procedure.
Checkable sources
- Measurement datum: distances measured from the mirror's back or holder rather than from the pole; a 7–8 cm offset would explain the cluster.
- Screen alignment: screen not perpendicular to the principal axis, or the image judged 'sharp' at its largest blur circle.
- Candle height: flame not at the principal axis, so the image is distorted and focus is misjudged.
- Mirror not vertical: the reflected image falls off-axis.
- Parallax and scale placement: eye not level with the scale; scale not along the axis.
- Room light: a dim image makes sharp focus hard to identify.
- Mirror thickness/aperture: a small, thick mirror gives a focus that depends on the aperture used.
What the teacher should do: repeat one measurement in front of the class, checking the datum, and compare the value measured from the pole with the value measured from the back of the mirror. If the difference is about 8 cm, the offset is confirmed. The class should then recompute. Calling the learners careless teaches them that physics is about matching a textbook number rather than about controlling variables.
2. Turn the discrepancy into a 15-minute lesson on error and experimental design.
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Minutes 1–3: Surface the anomaly. Write the eight group values on the board: 21, 22, 23, 23, 24, 22, 15, 16. Ask: 'Is this scatter random, or is something pulling the numbers one way?' Introduce random vs systematic error with those words.
Minutes 4–8: Test one hypothesis. Measure from the pole and from the back of the mirror. Record both. Ask students to subtract and explain the roughly constant difference. Define datum and parallax.
Minutes 9–12: Improve the method. Students list three changes: mount the mirror vertically, keep the candle flame at the axis, repeat and average. Show that averaging does not remove a systematic offset; only correcting the method does.
Minutes 13–15: Close with a quantitative check. Use 1/f = 1/v + 1/u with one corrected pair of readings; compare with the value obtained by focusing a distant window (approximately f). Ask each group to write one sentence: 'Our largest source of error was ___ because ___.'
This uses the failure as the content. The syllabus objective on mirrors is met more securely than by a correct demonstration copied from the board.
3. How should the teacher manage the single-apparatus constraint and assess process skills rather than one final number?
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Managing one set for 40 students
- Set up a circus of four stations: mirror measurement (10 minutes), ray-diagram drawing, error-analysis worksheet, and a calculation station applying 1/f = 1/v + 1/u to given data.
- Groups of five rotate every 10 minutes; the teacher stays at the mirror station, where the risk and the learning are highest.
- Train two student demonstrators from the Class 10 batch to run the ray-diagram station.
- Keep a laminated instruction card at each station so the teacher is not repeating instructions.
Assessing process, not the number
Use an observation checklist with four process indicators, each rated 0–2:
- Correct datum and scale alignment.
- Flame placed on the principal axis.
- At least two trials recorded before averaging.
- A written statement distinguishing systematic from random error.
Add a short viva: 'Why did you measure from here?' and 'What would you change next time?' The final calculated focal length is worth only one mark; the rest is process. This is fair to the group whose value was 23 cm but whose reasoning, after the lesson, is sound. It also fits the syllabus, because error analysis is an examinable skill in its own right.