One projector station, four possible arrangements and three different tests
Imagine a Secondary school preparing a projector demonstration for a learning fair. The source is a small printed word. A converging lens forms an inverted real image on a screen, and the students want visitors to be able to read the whole word. They have room for a short tabletop installation, not a full-size projection room. Four arrangements have been tested under a fictional classroom exercise. One gives a small but focused image. Another gives a larger image that fits. A third creates a dramatic picture too large for the available screen. The fourth is compact but still too small.
The choice looks straightforward until someone says, ‘The biggest image must be the best.’ Another student says that a clear image must be suitable for every visitor. A third writes, ‘Our projector guarantees perfect results.’ Each statement confuses a useful part of the evidence with a conclusion the evidence has not earned. Size, focus and readability are connected, but they are not the same property. The task is to keep their differences visible long enough to make a sound recommendation.
This is an integrated English, Mathematics and Science lesson, not an invented national examination paper. We will solve an original classroom case and then challenge twenty-eight claims that a writer or candidate could make about it. The case is deliberately fictional. Its figures are internally compatible with a simplified thin-lens model, but they are not measurements of an actual eduKateSengkang demonstration or of real visitors. A model is useful precisely when its assumptions can be inspected.
The official G3 SEC context in 2027
The first Singapore–Cambridge Secondary Education Certificate examination is held in 2027. According to the SEAB 2027 G3 syllabus directory, updated 26 October 2026, G3 English Language is K300 (formerly 1184), G3 Mathematics is K310 (formerly 4052) and standalone G3 Physics is K323 (formerly 6091). Consult the actual K300 English Language, K310 Mathematics and K323 Physics syllabuses for the requirements of each registered subject.
English K300 assesses Writing, Comprehension, Listening and Oral Communication. Mathematics K310 assesses reasoning and problem solving through two written papers, including application to a real-world scenario in its final Paper 2 question. Physics K323 includes light, converging lenses, image formation and practical investigation, assessed through multiple-choice, structured/free-response and practical components. Combined Science students have separately coded subject combinations and should check their own syllabus, not borrow every format or percentage from standalone K323.
EMS here means a teaching connection among English, Mathematics and Science. SEAB does not have a separate ‘EMS projector design’ assessment. A student should transfer the relevant skills to each real paper without pretending that the examination will reproduce this classroom case. All conclusions about the invented demonstration belong to our stated fictional brief.
One canonical owner for each kind of answer
Use Volume 0476: Physics Converging-Lens Screen Tests to learn what a focused real image is, why it can appear inverted and what a classroom screen observation can and cannot show. This EMS audit assumes that mechanism; it does not replace the foundational Physics explanation.
Use Volume 0477: Mathematics Projected-Image Geometry for the similar-triangle height ratio, inverse size calculations, margins, dimensions and inequalities. The current guide uses the calculations to make a decision rather than repeating the complete mathematical method. Use Volume 0478: English Exhibit Captions to repair unsupported promises, misleading comparators, inaccurate tenses and vague wording.
The preceding Volume 0475 periscope design review concerned reflection in plane mirrors, not focusing a real image with a lens. The earlier Vol 0317 refraction exhibition review concerned glass-block evidence and a different spatial model. These topics are related, but they have different claims to prove. Reusing the same subject label is not a reason to collapse the search intent of their owners.
Define the school requirement before checking the answer
The original printed label is 3 cm high and 5 cm wide. The usable screen measures 10 cm high and 16 cm wide. The organisers want the projected label to be at least 5 cm high but no more than 9 cm high, so that it can be read without cropping. The projected word must leave at least 1 cm of spare usable screen space at each side. Consequently, the image may be no wider than 16 − 1 − 1 = 14 cm.
The installation must fit within 120 cm of useful tabletop length. For this invented design brief, the class reserves 10 cm for stands and working clearance, in addition to the ideal object-to-lens distance u and lens-to-screen distance v. The first-stage length condition is u + v + 10 ≤ 120 cm. The 10 cm allowance is part of the hypothetical exercise, not a specification supplied by the Physics syllabus.
Finally, the school wants the projected word to be legible at a marked visitor position. That is an observational requirement, not a mathematical definition of image height. A projection can meet all the dimensions and remain too dim, blurred or difficult for some readers. We will treat focus, geometrical fit and legibility as three distinct tests.
The four fictional trial arrangements
The same object card, screen dimensions and idealised converging lens are used in all four arrangements. Trial A has object distance 40 cm and focused image distance 60 cm. Trial B has object distance 36 cm and focused image distance 72 cm. Trial C has object distance 30 cm and focused image distance 120 cm. Trial D has object distance 48 cm and focused image distance 48 cm. These distances are measured from a common lens reference for the idealised model.
The pairs are compatible with a thin lens of focal length 24 cm under the ideal relation between object and image distances: each pair gives the same reciprocal sum. The student does not need to memorise a thin-lens equation as part of the G3 Mathematics requirement to use the ratios below; treat the pairs as given focused arrangements. We mention consistency because it would be misleading to imply that any arbitrarily chosen u and v will both give a focused image with the same real lens.
For the first check, use the similar triangles formed by the object height, the optical centre and the real-image height. The positive linear magnification is v/u, and the image is inverted. The source image has height 3 cm and width 5 cm. The resulting image dimensions are calculated with the same scale factor in both directions.
Work through the numerical table in full
Trial A has magnification 60/40 = 1.5, so its image is 4.5 cm high and 7.5 cm wide. Its required bench length, with the stated fixture allowance, is 40 + 60 + 10 = 110 cm. It fits the width and bench restrictions but fails the minimum required image height, because 4.5 is less than 5. The Physics focus observation can be correct even though the visitor design fails.
Trial B has magnification 72/36 = 2. Its image is 6 cm high and 10 cm wide. It needs 36 + 72 + 10 = 118 cm of bench space. It satisfies the height interval of 5–9 cm, the permitted projected width of at most 14 cm and the maximum tabletop length of 120 cm. Its projected width leaves 3 cm spare at each side if the image is centred. Its bench margin is only 2 cm, which calls for a careful physical check.
Trial C has magnification 120/30 = 4. Its projected image would be 12 cm high and 20 cm wide, requiring 30 + 120 + 10 = 160 cm of bench space. It violates the height, width and length limits. Trial D has magnification 48/48 = 1, giving a 3 cm by 5 cm image and total layout demand of 48 + 48 + 10 = 106 cm. D is compact but fails the minimum projected height. Thus B is the only one of the four that passes all the stated geometric filters.
A geometrical pass does not guarantee readable text
Suppose the same ten student volunteers read the projected label at a marked viewing position in a brief fictional classroom trial. Four identify the word correctly with A; eight identify it with B. These numbers are counts of correct identification in a small exercise. They do not prove that B works for 80% of all future visitors. Reading order, memory of the word, room light, visual differences and the students’ viewing position may affect results.
A more useful follow-up test would use comparable words, a stated viewing distance, stable lighting and an order that reduces familiarity effects. A large group is not automatically a fair group; conditions still matter. The proposed display should also be checked for actual placement, because B leaves only 2 cm of margin in the simplified bench budget. No dimension on paper guarantees that a real stand will behave exactly like a point in a model.
At this stage the honest conclusion is conditional. B is the only arrangement that meets the stated numerical restrictions, and the invented short reading exercise gives encouraging but limited evidence. The school can select B for a supervised on-site check. It should not call B ‘perfect’, ‘certified’ or universally readable.
Twenty-eight original evidence-audit clinics
These short cases deliberately cross subject boundaries. Each begins with a plausible claim and tests it against the same fictional record or one explicitly changed condition. Try answering before reading the explanation. The question is not whether a sentence sounds impressive, but whether every part of it follows from the right piece of evidence.
01 — The largest option must win
Claim: ‘C is best because its image is four times larger.’
The stated scale factor is 4, but C produces a 12 cm by 20 cm picture and needs 160 cm of bench length. Every one of those relevant dimensions violates a stated limit. A result can be mathematically impressive yet practically unusable. The claim also blurs ‘four times the height’ with an unspecified meaning of ‘larger’.
Verdict: reject C for the stated brief; its scale is not the objective.
02 — A focused image is automatically suitable
Claim: ‘A is focused, therefore it passes the whole project.’
A can form a focused real image while producing only 4.5 cm image height. The minimum is 5 cm. Focus is a Physics success, but satisfying the visitor size criterion is a separate geometric requirement. There is no contradiction in saying that the image is clear and the design is too small.
Verdict: do not let one valid test replace the other tests.
03 — The screen’s nominal width
Claim: ‘All images fit because the screen is 16 cm wide.’
The usable width is 16 cm, but the brief reserves 1 cm at either side. The actual maximum projected width is 14 cm. Trial C produces 20 cm, so it fails even before height and bench space are considered. A careless comparison uses the wrong available quantity.
Verdict: subtract the stated margins before checking width.
04 — The wrong physical scale
Claim: ‘B fits because its source card is only 5 cm wide.’
The source is 5 cm wide but B’s projected image is twice that width, 10 cm. That still fits, yet the original reason does not support the decision. A right conclusion reached through an invalid comparison is fragile and will fail a more demanding problem.
Verdict: apply magnification to the dimension the screen receives.
05 — The fixture allowance disappears
Claim: ‘B uses 108 cm, leaving 12 cm spare.’
The sum 36 + 72 = 108 cm excludes the deliberately specified 10 cm allowance. The relevant installation length is 118 cm, leaving only 2 cm. The mathematical error is not difficult algebra; it is omission of a condition from the brief.
Verdict: include every specified component of the constraint.
06 — Focus is the same as brightness
Claim: ‘The brightest patch is necessarily the sharpest image.’
The classroom observation must be judged against recognisable detail. A bright but blurred patch does not establish that the small word is in focus. Image sharpness, brightness and reading accuracy can vary independently. Use the same specified feature when locating a usable image plane.
Verdict: define the physical result being measured.
07 — A normal optical result looks wrong
Claim: ‘B is defective because its projected word is inverted.’
Inversion is expected for the familiar real-image arrangements of a thin converging lens. It may require attention in the design of the source card or the presentation to visitors, but it is not itself evidence of faulty focus. A defect claim needs separate evidence.
Verdict: use the model before assigning a fault.
08 — A rate from ten people becomes a universal rule
Claim: ‘B will work for 80% of everyone.’
Eight of ten volunteers reading one word correctly gives 80% in that particular trial. It is not a statistically justified population prediction. The result may reflect familiarity, lighting and the specific ten volunteers. A caption should preserve the actual denominator and context.
Verdict: report eight of ten students in the test, not 80% of all visitors.
09 — A percentage becomes a guarantee
Claim: ‘Because eight of ten succeeded, every group of ten will have eight successes.’
A frequency observed once is not a deterministic rule for future groups. Even with a fairer sampling design, the result would come with uncertainty. The simple correction is to distinguish the completed trial from future expectations.
Verdict: keep observation and prediction separate.
10 — The wrong ratio
Claim: ‘B’s magnification is 36 divided by 72, or 0.5.’
That reverses the roles of object and image distances in the positive similar-triangle size relation. The correct ratio is v/u = 72/36 = 2. The source height of 3 cm therefore gives a 6 cm image. A simple sketch can catch a reversed fraction before more numbers are calculated.
Verdict: identify which triangle represents the projected image.
11 — A larger image has a doubled area
Claim: ‘B doubles the height, so it doubles the occupied area.’
Both corresponding linear dimensions double in the ideal scale model. The source area is 3 × 5 = 15 cm², while B’s projected area is 6 × 10 = 60 cm². The area scale factor is four, not two. This does not replace the separate height and width checks.
Verdict: distinguish length ratios from area ratios.
12 — A false technical diagnosis
Claim: ‘B is better because it has a stronger lens than A.’
The fictional record uses the same lens at different object positions. The different image heights result from geometry. The trial does not establish different material quality or optical power. ‘Stronger’ has no clear measurement here. The prose should identify the property actually compared.
Verdict: describe the arrangement, not an unmeasured lens characteristic.
13 — Incorrect precision
Claim: ‘The best focus is exactly 72.0000 cm.’
We used 72 cm as a given focused position. No measurement resolution was supplied to support four decimals, nor is ‘best’ defined across repeated practical trials. Writing more digits does not create experimental certainty.
Verdict: express the result with precision supported by the data.
14 — The average of incompatible choices
Claim: ‘A and C average 8.25 cm in image height, so together they meet the height criterion.’
Their heights are 4.5 and 12 cm, whose arithmetic mean is 8.25 cm. But the school must select an individual arrangement. Neither A nor C meets all constraints, and averaging their heights cannot make either suitable. The numerical mean answers a different question.
Verdict: test candidates individually rather than averaging feasibility.
15 — A claimed comparison without common conditions
Claim: ‘B is easier to read because B used bold lettering.’
If the word changed between A and B, source boldness could explain a reading difference. The original fictional comparison assumes the same source card. A modified source creates a new trial and needs a new fair comparison; it cannot be quietly blended with the old record.
Verdict: identify the tested variable and what stayed constant.
16 — A missing unit
Claim: ‘B’s screen distance is 72 and its height is 6.’
The first quantity is 72 cm from lens reference to screen, while the second is 6 cm of projected image height. Bare numbers leave those meanings hidden. Different measurements can share a unit without being interchangeable.
Verdict: attach every number to its physical endpoints.
17 — A frame counted twice
Claim: ‘The screen is 16 cm usable and needs another 4 cm deducted for the old frame.’
If the 16 cm is already specified as usable width, the frame has already been accounted for. Deducting it again changes the brief. If a new screen specification instead says 16 cm nominal with a 2 cm frame on each side, then the usable width is 12 cm and all candidates should be retested under that new condition.
Verdict: never subtract a margin twice.
18 — An extra margin changes the result
Claim: ‘B will fit even if the school now requires 4 cm clear on each side.’
With this revised brief, the maximum allowable width is 16 − 8 = 8 cm. B projects 10 cm. B would fail the new requirement despite passing the original. A correct response updates the decision when a controlling condition changes.
Verdict: do not reuse a conclusion after changing its assumptions.
19 — A new minimum letter height
Claim: ‘B still wins if the minimum image height becomes 7 cm.’
B gives 6 cm, so it fails the revised minimum. C gives 12 cm but fails the maximum height, width and bench conditions. The current four choices may all fail. The honest result is ‘none of these candidates’, not a forced selection.
Verdict: consider whether a feasible option exists before ranking.
20 — Repair one limit and ignore the others
Claim: ‘A wider screen makes C valid.’
Even if the screen accommodates C’s 20 cm projected width, C is still 12 cm high where the maximum is 9 cm and needs a 160 cm layout where the limit is 120 cm. Removing one violated condition does not remove the remaining ones.
Verdict: recheck the complete constraint set.
21 — A rounded limit creates the wrong verdict
Claim: ‘B needs about 120 cm, so it exceeds a 120 cm maximum.’
The exact sum from the given figures is 118 cm, which is within the limit. Rounding it prematurely to 120 can hide its margin, but even 120 would meet a ‘no more than 120 cm’ rule. The student should compare the unrounded result and read the inequality accurately.
Verdict: keep exact sums until after the threshold decision.
22 — The model predicts human comfort
Claim: ‘A 6 cm letter guarantees every visitor can read.’
Six centimetres is an image dimension. It does not measure room lighting, viewing distance, the content of the letters or the visual abilities of every visitor. A separate reading observation is required, and even that observation has a limited audience and setting.
Verdict: do not convert geometry directly into a universal human outcome.
23 — A practical observation becomes an official endorsement
Claim: ‘SEAB has approved this projector as the required G3 SEC experiment.’
The Physics syllabus contains lens topics and relevant practical reasoning, but a fictional classroom design is not thereby an officially approved national practical task. Examination scope and locally chosen teaching activity must remain separate.
Verdict: attribute official statements only to the official document that actually makes them.
24 — A test that did not happen
Claim: ‘We have verified the public installation’ when only a classroom bench was used.
The classroom measurements support a preliminary decision. A real on-site check for available space, mounting and reading conditions is still needed. A future activity cannot be described as completed by changing the tense of the sentence.
Verdict: distinguish planned, classroom-tested and site-verified stages.
25 — Misleading word ‘all’
Claim: ‘All the printed text is visible’ when one letter is clipped.
The completeness condition is binary under the brief: the whole label must fit. Recognising the word from context is not the same as seeing every letter. State the clipping and adjust the layout, source size or allowed constraints rather than pretending a partial projection is complete.
Verdict: report the observation rather than the likely guess of a reader.
26 — An untested cause for readability
Claim: ‘B’s higher reading count was caused only by its larger image.’
Image size is a plausible factor but not the only possible factor. The order of tests and word familiarity may influence results. A stronger design could randomise or counterbalance the order and keep the printed target and lighting comparable.
Verdict: qualify a causal explanation until competing explanations have been addressed.
27 — A sloppy comparative caption
Claim: ‘B is clearly the best and most professional setup.’
Those adjectives do not name a criterion. A defensible caption is: ‘Among the four arrangements tested, B alone met the stated image-size and table-length limits.’ This identifies the comparison set, evidence and scope. Readability remains subject to a further fair test.
Verdict: replace vague superiority with the actual decision criterion.
28 — A final visitor message
Claim: ‘Our extraordinary lens delivers perfect giant images for every audience.’
An evidence-safe revision is: ‘In our classroom trial, Arrangement B formed a focused, inverted image that met the stated screen and tabletop limits. We will check the public display’s reading conditions before the event.’ That is clear, useful and truthful without being dull.
Verdict: write the strongest claim the evidence supports, not the strongest imaginable slogan.
Compose a decision brief a teacher can actually use
A short recommendation can begin with a verdict rather than a long history: ‘We recommend Trial B for the supervised final setup check.’ This is better than ‘B is the best ever’ because it names a specific next action and does not pretend that every practical requirement has already been tested. The brief then gives the numerical reason: ‘With the 3 cm by 5 cm source card, B projects a 6 cm by 10 cm image and needs 118 cm of bench length including the stated allowance.’
Follow with the constraints: ‘The image is within the required height range of 5–9 cm, leaves 3 cm horizontal margin on each side if centred, and fits the 120 cm maximum table length.’ Then disclose the limitation: ‘In the preliminary reading exercise, eight of ten volunteers identified the printed word at the marked viewing position, but further testing is needed to establish a reliable public arrangement.’
Each sentence serves a reader. The first is the recommendation; the second records the result; the third proves feasibility; the fourth explains what is still unknown. The brief is longer than a label but much shorter than a laboratory report. It can guide the school without allowing an attractive display to conceal a weak assumption.
How to explain the same case in three different examination responses
In a Physics response, start with whether the screen intercepts a real focused image. Describe the role of image plane and why a movement away from the best screen position can cause blurring. If a ray diagram is requested, include the relevant principal rays and image orientation. Do not add a long explanation about visitor survey results when the question is only about light.
In a Mathematics response, start with similar triangles or the supplied image-size relation, then calculate the projected dimensions and compare them with the stated inequalities. A response that finds m = 2 but never answers whether the screen fits is unfinished. Likewise, if the problem gives a new margin, the student must recalculate the usable region before selecting an option.
In an English task, the challenge may be to interpret a promotional caption, identify the writer’s effect, or draft a responsible note to visitors. Use the evidence accurately, but let purpose, audience and context govern how much technical detail appears. A Physics equation may support a conclusion behind the scenes without needing to appear in a public caption. This is transfer of discipline, not a demand to make every subject identical.
A week of deliberate practice from foundations to integration
On day one, write the four conditions from the design brief without doing arithmetic. Then reread each for words such as ‘at least’, ‘no more than’ and ‘usable’. On day two, reconstruct the projected dimensions from the positive ratios. Check units and whether the height is above or below the source height. On day three, compare each candidate with all dimensions and the full bench-length rule.
On day four, write the legitimate Physics finding and the scientific limitation in separate sentences. On day five, revise five bold publicity claims into evidence-safe labels with a specified audience. On day six, change a single condition, such as the minimum height or required side margin, and explain why the decision may change. On day seven, write a complete recommendation under a word limit without omitting an essential constraint.
If an answer goes wrong, do not label the whole student weak. Trace the first error. Was a width compared with a height? Was a measurement treated as a prediction? Was a small sample turned into a universal promise? Repair that particular habit and try a new example. This is the progression from basic representation towards controlled examination performance.
Continue the verified learning routes
Students returning from PSLE may begin with the earlier guide on naming the decision and the PSLE Learning Guide. For the necessary subject foundations, use Volume 0476 Physics, Volume 0477 Mathematics and Volume 0478 English in order. The Mathematics Hub, Science Hub and Secondary English Learning Hub provide wider owner routes.
The actual national examination facts belong to SEAB’s current G3 directory, English K300, Mathematics K310 and Physics K323. The integrated project is a learning exercise: no official EMS paper is claimed, no specific examination question is predicted, and no fictional volunteer count is represented as a real-world study. The last habit worth keeping is also the simplest: an attractive answer remains incomplete until every relevant condition and every important word has been checked.
