Science 7–10 · Year 7
Sun angle and energy per square metre: a torch on graph paper
Science understanding: Earth and space sciences (NSW Stage 4 focus area: Observing the Universe)
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The idea
The same beam spread over a larger patch delivers less energy to each square metre, which is why a low winter Sun warms the ground less than a high summer Sun.
What you need
- 1 torch with a narrow beam, or a clamped desk lamp with a cardboard tube collimator
- 1 sheet of 1 cm graph paper taped to a board
- 1 protractor and 1 retort stand with clamp to hold the torch at a fixed distance
- 1 digital thermometer or datalogger probe taped under black paper (optional heating run)
- 1 pencil to trace the lit patch
How to do it
- Clamp the torch 30 cm from the paper pointing straight down (0 degrees from the vertical) and trace the lit patch; count the whole squares inside it.
- Tilt the board by 30, 45 and 60 degrees, so the beam meets it at those angles from the perpendicular, keeping the beam centre on the same point and the torch-to-paper distance along the beam unchanged; trace and count each patch.
- Record the count for each angle in a table and plot squares against angle; compute 1 / cos(angle) for each angle and compare.
- Optional heating run: tape the probe under black paper, shine the beam for 5 minutes at 0 degrees and again at 60 degrees from a cold start, and record the temperature rise each minute.
- Run three traces per angle and use the mean count.
What you should see
The patch area grows as 1 / cos(angle): relative to the 0 degree patch the counts come out near 1.15 at 30 degrees, 1.41 at 45 degrees and 2.0 at 60 degrees, so energy per square centimetre at 60 degrees is half the overhead value. In the heating run the black paper under the 60 degree beam should warm at roughly half the rate of the overhead beam at the start, because it receives half the energy per square centimetre. The size of the rise depends on the lamp: an LED torch may warm the paper very little, so a filament desk lamp gives a clearer run, and heat lost to the air makes the ratio less clean than the area count. The ratio, not the absolute rise, is the result. The learner knows it worked when the counts sit within 10 percent of the 1 / cos(angle) line.
What changes
- What you change
- angle of the beam from the vertical
- What you measure
- area of the lit patch (and temperature rise per minute)
- What you keep the same
- torch to paper distance along the beam
- torch brightness
- room lighting
- paper colour
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Summer is warmer because Earth is closer to the Sun; Earth is nearest the Sun in early January, during the southern summer and northern winter.
- A tilted surface receives less light because it is further from the source; the distance along the beam is unchanged and the spreading is what matters.
Safety card
Hazards
- warm lamp housing if a mains lamp is used
Controls
- use a battery torch or let a mains lamp cool before handling
- do not stare into the beam
Note
No hazardous chemical and no flame or heating apparatus: a generic classroom risk assessment (CSIS 1.7 or RiskAssess) covers trips, spills, warm lamps and sharp edges.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Science 7-10 Syllabus (2023), NSW Education Standards Authority (implemented from 2026; codes read at curriculum.nsw.edu.au on 22 and 23 September 2026)SC4-OTU-01SC4-WS-01SC4-WS-04SC4-WS-05
- Australian Curriculum v9AC9S7U03AC9S7I02AC9S7I04
Sources
The pages the author read to write this activity.