Does light really follow an inverse-square law?

AA SLAI SL Accessible Also in: Statistics

Research question

Does the illuminance measured by my phone fall as 1/d² as I move away from a lamp, and at what distances does the model fail?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

The inverse-square law is fundamental to light, sound and gravity, and your phone contains a light sensor. Testing it — and finding where it breaks down (near the bulb, with reflections) — is a clean, personal experiment.

The mathematics you'll need

Power models and inverse variation
Log-log linearisation
Residual analysis
Transformations for background light

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

In a dark room, measure illuminance with phyphox's light sensor at 20+ distances from a small bulb, three readings each; record background light.

phyphox (RWTH Aachen) — Free app that turns your phone's accelerometer, microphone, barometer and gyroscope into data loggers with CSV export.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Explain why intensity should fall with 1/d² from geometry.
Collect data, subtracting background light.
Fit y = axⁿ via logs and compare n with −2.
Examine residuals close to and far from the bulb.
Reflect on the sensor, reflections and the bulb not being a point source.

Pitfalls that cost marks

Measuring from the wrong point (the sensor position on the phone matters).
Ignoring background light.
Only testing over a narrow range of distances.

Showing personal engagement

Compare an LED and an incandescent bulb.
Use your model to design desk-lamp placement for a target lux level.
Explain the discrepancy near the bulb with a finite-source model.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Model the bulb as a line or disc source and show how the inverse-square law emerges at large distances.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).