中文（繁體）
中文（简体）
English
P3 General Studies: Light and Shadows (Paper 3 (challenge))
Tutor Prep Guide · straight-line light, shadow direction and length, reflection angles and the normal, sundials and pinhole images
P3 General Studies: Light and Shadows (Paper 3 (challenge))
Paper three puts shadows and reflection into one right-triangle model, practising tangent, inverse tangent and surface-angle conversion.
Direct answers Draw the right triangle and label the three quantities before choosing tangent or a subtraction from 90 degrees.
01 Paper details (check answers afterwards)
| Item | Detail |
|---|---|
| Questions | 10 |
| Suggested time | 20 |
| Difficulty mix | Foundation 3 · Intermediate 3 · Challenge 3 · Error redo 1 |
| Chapter | Chapter: P3 General Studies: Light and Shadows |
| Level | parts of a closed circuit, conductors against insulators, series against parallel, adding up battery voltage, and electrical safety |
02 Questions (10 items)
- FoundationWhen the ratio of height to shadow length is 0.75, what is the angle of the sunlight to the ground?
- FoundationA 1.8 m object casts a 2.4 m shadow. What is the ratio of height to shadow length?
- FoundationThe incoming ray makes 65 degrees with the mirror surface. What is the angle of incidence?
- IntermediateWith a 1 m object and a 3 m shadow, what is the angle of the sunlight to the ground?
- IntermediateA periscope uses two 45 degree mirrors. How far is the ray turned in total?
- IntermediateFour 45 degree mirrors are placed in line. How far is the ray turned in total?
- ChallengeWhat does a long shadow on slanting sunlight have to do with light travelling straight?
- ChallengeWhy can a sundial tell the time?
- ChallengeHow many colours are there in a rainbow from outside to inside?
- Error redoA classmate divides shadow length by height (2 over 1.5) and calls it the height to shadow ratio. What is wrong?
03 Answers and one-line notes
| # | Answer | One-line note |
|---|---|---|
| 1 | 36.9 degrees | The tangent of the angle is 0.75, and the inverse tangent gives 36.9 degrees. |
| 2 | 0.75 | One point eight divided by two point four equals 0.75. |
| 3 | 25 degrees | The normal is 90 degrees to the surface, and 90 minus 65 gives 25 degrees. |
| 4 | 18.4 degrees | The tangent is one third, so the angle is 18.4 degrees, a very slanting ray. |
| 5 | 180 degrees | Each mirror turns the ray 90 degrees, so the two together turn it 180 degrees. |
| 6 | 360 degrees | Each mirror turns the ray 90 degrees, so four turn it 360 degrees and the ray returns to its original direction. |
| 7 | The blocked dark region stretches along the ground | Because light travels straight, a slanting ray leaves a dark region stretched along the ground, so the shadow lengthens. |
| 8 | The Sun moves, so the shadow changes direction and length | Straight-line light plus the moving Sun makes the gnomon shadow shift in direction and length hour by hour. |
| 9 | 7 colours | Red, orange, yellow, green, blue, indigo and violet make seven colours. |
| 10 | The terms are inverted; the ratio is height divided by shadow length | Height to shadow ratio means height over shadow, so 1.5 over 2 gives 0.75; inverting it gives 1.33 and a wrong angle. |
04 What to do after marking
- After marking, redo only the wrong items and write down which step went wrong (formula, unit, or misread number).
- Repeat the same item two days later; move to the next paper only when both attempts are correct.
- Parents only need the answer and note columns; there is no need to explain every item.
Paper four clears the conductor, insulator and battery direction misconceptions.Tutor Registration →
Questions and answers are written originally by the TutorZone team and are not taken from any school, publisher or examination authority paper. Every value is checked by computer.