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Science project idea

Inverse square law of light with an LED and a phone lux meter

The brightness of a small light source falls with the square of the distance. Doubling the distance cuts the light to a quarter.

Make it yourself7 numbered steps, the materials and the science, all free.Go to the stepsGet a ready-made kitReady-made models, kits and spare parts in the store under Physics.Browse PhysicsAsk on WhatsAppAsk the head office whether a model or kit for this idea is available.Send a message

What it shows

The brightness of a small light source falls with the square of the distance. Doubling the distance cuts the light to a quarter.

The science

A point source sends its light out in all directions, and the same amount of light spreads over a sphere of area 4πd² at distance d. The intensity (power per unit area) is therefore I = P / 4πd², proportional to 1 / d². A plot of I against 1 / d² is a straight line through the origin. Stray light and a source that is not small compared to d make the line curve, which is why the room must be dark and the readings taken beyond about 20 cm.

Materials

Cost: free. Many items come from home or from waste; spare parts such as LEDs, motors and wire are in the store.

  • A small bright LED torch or a single LED on a battery, as a point source
  • A smartphone with a lux meter app, or an LDR and a multimeter
  • A long table or a floor with a metre tape
  • A dark room or a night-time corridor
  • Black cloth or paper to cut reflections
  • Graph paper

Safety

For this project: Do not look directly at a bright LED from close range. An adult should supervise if a phone is held on a tape.

Never use mains electricity: power models with cells, batteries or a low-voltage adapter. Sharp and hot tools, flames and lab chemicals need an adult or your teacher beside you. Keep magnets, button cells and small parts away from young children, and wash your hands after making.

All the safety rules

Step by step

7 steps. Do them in order, and test each part before you go on to the next. Write what you notice in a notebook as you go.

  1. Darken the room as far as you can and lay the tape along the table with the source at the 0 mark.

  2. Hold the phone light sensor (usually near the front camera) facing the source and read the lux value with the source off; this is the background reading.

  3. Switch on the source and read the lux at 20, 30, 40, 50, 60, 80 and 100 cm.

  4. Subtract the background from every reading.

  5. Calculate 1 / d² for each distance in a table with d, lux and 1 / d².

  6. Plot lux (y) against 1 / d² (x) and see that the points lie on a straight line through the origin.

  7. Check the doubling rule directly: compare the reading at 40 cm with the reading at 20 cm.

What you should see

Lux against 1 / d² is a straight line, and the reading at double the distance is about one quarter. Small deviations near 20 cm come from the source not being a true point.

Viva questions

A teacher or a judge will ask how it works. Try to answer each question before you open it, then compare.

1What happens to the intensity when the distance is tripled?

It becomes one ninth.

2Why does the light spread out as the square of the distance?

The same light covers a sphere whose area grows as the square of the radius.

3Why subtract the background reading?

The sensor also picks up stray light that has nothing to do with the source.

4Does the same law apply to gravity?

Yes, the gravitational force from a point mass also falls as 1 / r².

Free ebook: Viva Questions for Science Projects

Take it further

Compare a white LED and a red LED of equal brightness and find whether the law holds for each.

Change one thing, measure what happens, and add a table or chart of your readings: that is what turns a model into your own investigation.

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