Investigating Science 11–12 · Year 11
Distance and exposure: the inverse square law measured with light
Module 4: Theories and Laws
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The idea
Intensity from a small source falls with the square of the distance, a law whose predictions a measurement can test, and the reason distance from a radiation source is a basic way to reduce exposure.
What you need
- a bare LED or a small bare low-voltage lamp with no reflector or lens in front of it; not a torch, whose reflector or lens narrows the beam so that its reading does not fall as 1/d² measured from the emitter
- a lux meter or a phone running the phyphox light experiment, metre rule, a darkened room
How to do it
- Measure the background light with the source off.
- Measure the intensity at 0.20, 0.30, 0.40, 0.60, 0.80 and 1.00 m from the emitter, three readings each.
- Subtract the background and plot intensity against 1/d².
- Check whether doubling the distance quarters the reading, and find where the law breaks down close to the source.
- Apply the result to radiation protection: how exposure changes when a worker moves from 1 m to 2 m from a small source, and why regulation specifies distances.
What you should see
After background subtraction, the reading at 0.40 m is a quarter of that at 0.20 m and at 0.80 m a sixteenth; the intensity against 1/d² graph is a straight line through the origin, departing from it only very close to the source, where the emitter is no longer point-like. The quarter and sixteenth ratios hold only for a bare source; a torch's reflector gives readings that fall more slowly than 1/d², which the learner can show by repeating the run with a torch. For a small radiation source the same law means moving from 1 m to 2 m cuts the exposure rate to 25 %, and to 4 % at 5 m.
What changes
- What you change
- distance from the source
- What you measure
- light intensity (lux)
- What you keep the same
- same source and battery
- meter facing the source
- background measured and subtracted
- room kept dark
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Intensity halves when the distance doubles.
- Radiation fills a room evenly.
- Shielding is the only way to reduce exposure.
Safety card
Hazards
- bright LED close to the eyes
- moving in a darkened room
Controls
- do not look into the emitter at close range
- clear the floor before darkening the room
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.
- Investigating Science Stage 6 Syllabus (2017), NESA; currentINS11-11INS11/12-5INS11/12-6INS11/12-7
- Australian Curriculum v9No Australian Curriculum v9 code is listed.
Sources
The pages the author read to write this activity.