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Earth and Environmental Science 11–12 · Year 11

Angle of sunlight and energy received: the cosine law with a lamp and a light meter

Module 3: Energy Transformations

Practical, model not builtLow risk

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The idea

The energy a surface receives per square metre falls with the cosine of the angle from the perpendicular, which is why latitude, season and axial tilt control climate.

What you need

  • desk lamp on a stand as the Sun, 1 m from the target
  • light meter (lux) or a small solar cell with a multimeter, mounted on a board with a protractor hinge
  • black card target and a thermometer taped behind it for the temperature version
  • globe on a tilted axis for the seasons demonstration (Earthlearningidea Seasons)

How to do it

  1. Set the board perpendicular to the lamp (0 degrees) and record the lux (or the solar-cell current).
  2. Tilt the board in 15 degree steps to 75 degrees and record at each; take three readings per angle.
  3. Plot reading against cos(angle); fit a straight line through the origin.
  4. Repeat by temperature: record the target temperature after 5 minutes at 0, 30 and 60 degrees.
  5. On the tilted globe, show which hemisphere faces the lamp squarely at each solstice and relate this to the plot.

What you should see

The reading follows cos(angle): 0.866 of the perpendicular value at 30 degrees and 0.500 at 60 degrees, provided the lamp-to-board distance is held fixed and the meter responds to the cosine of the angle of incidence. The 60 degree target warms more slowly than the perpendicular target in the same time. On the globe, the hemisphere tilted toward the lamp receives near-perpendicular light in its summer.

What changes

What you change
angle between the surface normal and the lamp
What you measure
illuminance (lux) or solar-cell current; temperature rise
What you keep the same
  • distance from lamp to the pivot
  • lamp power
  • room light excluded
  • reading time

Common misconceptions

Each of these ideas is wrong, and the activity is a chance to test it.

  • Summer is warmer because the Earth is closer to the Sun.
  • The Sun is directly overhead at noon everywhere in summer.

Safety card

Low riskLearners carry it out

Hazards

  • hot lamp housing

Controls

  • do not touch the bulb
  • lamp on a stand

Note

No hazardous chemicals or heat sources: record the activity in the school's RiskAssess risk assessment, following the NSW Department of Education Science safety and compliance page; the Chemical Safety in Schools package is not triggered.

Curriculum references

The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.

  • Earth and Environmental Science Stage 6 Syllabus (2017), NESA; current, replaced by the 11–12 Syllabus (2025) from 2028EES11-10EES11/12-5EES11/12-6EES11/12-7
  • Earth and Environmental Science 11–12 Syllabus (2025), NESA; to be implemented from 2028, not yet taughtEES-12-03
  • Australian Curriculum v9No Australian Curriculum v9 code is listed.

Sources

The pages the author read to write this activity.

  1. www.nsw.gov.au/education-and-training/nesa/curriculum/science/earth-and-environmental-science-stage-6-2017
  2. www.earthlearningidea.com/PDF/193_Seasons.pdf
  3. www.earthlearningidea.com/PDF/191_Hot_or_not.pdf
  4. nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html

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