Inverse Square Law Virtual Lab: Light Intensity and Distance

This inverse square law virtual lab turns the light-meter practical into a clean, quick data set. A small lamp acts as a point source, and students move a lux meter from 0.20 m to 1.00 m along a rule. With the room lights on, they first record the background with the lamp off, then subtract it from every reading. A graph of E − B against 1/r² gives a straight line through the origin, and lg(E − B) against lg r gives a gradient of −2. Every value below was read from the simulation.

Curriculum links

• NSW HSC Physics, Module 3 (Waves and Thermodynamics): the inverse square law for the intensity of light from a point source.
• AQA GCSE Physics (physics only): waves can be reflected, absorbed or transmitted at a boundary, used here in the Materials extension.
• Key Stage 3 science in England (light waves): transmission of light through materials, absorption, diffuse scattering and specular reflection.

Simulic is not affiliated with or endorsed by NESA, AQA or the Department for Education.

Before the lab (5 min)

Ask students to commit to a prediction, on paper or as question 1 of the class link:

"With the room lights off, the light meter is moved from 0.30 m to 0.60 m from the lamp. What happens to the reading?"

Many students choose "it halves".

Method in the simulation

1. Click the Distance tab. Keep Luminous intensity I at 40 cd and tick Room lights on.
2. Untick Lamp on and press Record. This is the background B. Tick Lamp on again.
3. Set Distance r to 0.20 m (or drag the meter) and press Record.
4. Repeat at 0.30, 0.40, 0.50, 0.60, 0.80 and 1.00 m. The table works out E − B, 1/r², lg r and lg(E − B).
5. Set Graph to E − B against 1/r², then to lg(E − B) against lg r, and copy the best-fit line each time.

r (m)	0.20	0.30	0.40	0.50	0.60	0.80	1.00
E (lux)
E − B (lux)
lg r
lg(E − B)

Expected results

Readings fluctuate by about ±0.4%, so groups differ slightly. On a freshly opened page:

r (m)	0.20	0.30	0.40	0.50	0.60	0.80	1.00
E (lux)	1014	459	266	175.5	125.9	77.7	55.0
E − B (lux)	999	444	251	160.7	111.1	62.9	40.2

• Background: B = 14.8 lux (the room lights add 15 lux).
• E − B against 1/r²: E − B = 39.9 × (1/r²) + 0.6, so I ≈ 39.9 cd.
• Log–log graph: lg(E − B) = −2.00·lg r + 1.60, so the gradient is −2 and I = 10^1.60 ≈ 40.2 cd.
• Without the background reading: the same distances gave a log–log gradient of −1.81, and the 1/r² line crossed the axis at 16.5 lux.
• Prediction check (room lights off): 440 lux at 0.30 m and 111.0 lux at 0.60 m, a quarter.

Questions for students

1. (Prediction, asked again after the lab) What happens to the reading when r doubles from 0.30 m to 0.60 m?
2. Which variable must stay the same?
3. With the room lights on, what does the meter record at r = 0.50 m?
4. What is the gradient of your graph of lg(E − B) against lg r?
5. Why do you record the background and subtract it?

Answers for teachers: (1) It falls to a quarter. (2) The lamp's luminous intensity I (and the room lighting). (3) Accept 172–178 lux. (4) Accept −2.05 to −1.95. (5) The room lights add about 15 lux to every reading. That matters most far from the lamp, so uncorrected data fall off too slowly (gradient −1.81 instead of −2.00); E − B leaves only the lamp's light, E = I/r².

Common misconceptions

• "Twice as far, half as bright." The light spreads over four times the area, so 0.30 m to 0.60 m drops the reading from 440 to 111 lux.
• "Background light is too small to matter." At 1.00 m, the 14.8 lux of background is more than a quarter of the 55.0 lux reading.
• "A straight line means proportional." E against r is a steep curve; only E − B against 1/r² is a straight line through the origin.

Extension

On the Materials tab (beam at 30° to the normal, meter at φ = 30°): the empty holder read 991 lux, clear glass 909 lux and frosted glass 57.7 lux behind the sample. In front, a plane mirror read 902 lux at 30° and 0.0 lux at 60°, while matt white card read 27.7 lux at 30° and 32.0 lux at 0°. Ask students to explain specular and diffuse reflection from these numbers.

FAQ

Can the class link open on the Distance tab?

Yes. In the link's starting values, set Screen to Distance: inverse square law and tick Room lights on. Keep Luminous intensity of the small lamp I at 40 cd so the answers match.

Why does the meter flicker?

The model adds a small fluctuation, like a real meter. Recorded readings are seeded: reloading or pressing Reset repeats them.

Why is the gradient of E − B against 1/r² equal to I?

Because E = I/r², with E in lux, I in candela and r in metres. The fitted 39.9 cd is within 0.3% of the lamp's 40 cd.

Related simulations and guides

Geiger counter lab – absorption of α, β and γ radiation and the inverse-square law Color vision – mixing light and color filters

The same 1/r² law appears for gamma rays in the radiation absorption virtual lab. For another light-meter practical, see the Malus's law virtual lab.