How Does Distance from a Light Source Affect Brightness? An Easy Home Experiment

Overview

When you stand farther from a lamp, the light looks dimmer. The reason is the inverse‑square law: the illuminance (brightness) on a surface falls off in proportion to the square of the distance from the source. In other words, doubling the distance makes the light four times weaker.^[1][2][3] This experiment lets children see that relationship for themselves.

Before You Begin

• Choose a quiet, dim room so ambient light does not overwhelm the measurements.
• Make sure the light source stays on for the entire test (use a lamp with a stable power supply).
• If you use a smartphone light‑meter app, calibrate it by first measuring a known reference (e.g., a bright window) and noting the reading – you will compare relative changes, so exact calibration is not critical.
• Adult supervision is needed when handling electrical cords or a hot bulb.

Materials

• One 40‑watt incandescent bulb (or any steady‑state lamp) mounted in a lamp socket.
• Ruler or tape measure (centimetre or inch marks).
• Light‑meter device – a cheap handheld lux meter works well, or a smartphone with a free illuminance app.
• Notebook or worksheet for recording data.
• Cardboard or paper (optional) to create a simple screen that blocks stray light.

Testable Question

How does the measured illuminance change as the distance between the light source and the sensor is increased?

Hypothesis

As the distance doubles, the measured illuminance will become about one‑quarter of its previous value, following the inverse‑square law.

Variables and Controls

Procedure (Steps)

1. Set the lamp on a stable table and turn it on. Let it warm for a minute so the output stabilises.
2. Place the light‑meter sensor directly in front of the bulb, with its front facing the lamp.
   • Measure the distance from the centre of the bulb’s filament to the centre of the sensor using the ruler. Record this as the first distance (e.g., 20 cm) and note the lux reading.
3. Move the sensor straight away from the bulb to a new distance (e.g., 40 cm). Record the distance and the new lux reading.
4. Repeat the move‑and‑record steps for at least five distances, ideally doubling each time (20 cm, 40 cm, 80 cm, 160 cm, 320 cm) if space allows. If the room is small, use smaller increments (e.g., every 10 cm) but keep the spacing consistent.
5. For each distance, perform two trials: remove the sensor, return it to the same spot, and record the reading again. This checks repeatability.
6. When finished, turn off the lamp and safely store the equipment.

What to Observe or Measure

Record the following in a table:

• Distance (cm)
• Lux reading (first trial)
• Lux reading (second trial)
• Average lux for that distance

Notice how the numbers shrink as the distance grows.

Data Table (Blank)

Graphing Your Results

Plot a graph with distance (cm) on the horizontal axis and average lux on the vertical axis. A smooth curve that drops quickly shows the inverse‑square relationship. For a clearer visual, also plot distance squared (d²) on the x‑axis; the points should line up roughly straight, confirming that lux ∝ 1/d².

The Science Explained

Light spreads out in all directions from a point source, forming expanding spheres. The same amount of luminous energy passes through each larger sphere, but the surface area grows as the square of the radius (A = 4πr²). Because the energy is spread over a larger area, the amount that reaches any tiny patch of a surface drops with the square of the distance. This is the inverse‑square law, expressed mathematically as:

E = I / d²

where E is illuminance (lux), I is the source’s luminous intensity, and d is distance. The law holds well when the distance is at least five times the size of the source, a rule of thumb used in lighting design.^[3]

Common Misconceptions

• “Brightness just gets weaker linearly.” – It actually drops much faster; double the distance makes it four times dimmer.
• “Any lamp follows the law exactly.” – Real lamps are not perfect point sources; at very short distances the law deviates because the bulb’s size matters.

Troubleshooting

• If readings do not decrease smoothly, check that the sensor stays directly in line with the bulb; any sideways shift changes the effective distance.
• Ambient light can add a constant offset. Reduce room lights or cover the setup with a cardboard shield.
• Make sure the bulb does not cool down between measurements; a hot bulb can be brighter.

Try Another Version

Replace the incandescent bulb with an LED torch or a smartphone flash. Compare how the slope of the distance‑vs‑lux curve changes with different light‑source designs. This extension introduces the idea of “luminous efficacy” – how much light a source produces per watt of electricity.

Cleanup and Disposal

Turn off and unplug the lamp. If you used a disposable light‑meter, store it for future use. Re‑cycle the cardboard shield if you made one.

Next Steps

Use the measured relationship to calculate how bright a streetlamp would appear from a window, or to design a simple “light‑controlled alarm” that triggers when a room gets too dark.