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Science project idea

Shadow size against torch distance: similar triangles at home

Light travels in straight lines, so the shadow of an object grows larger as the torch moves closer. Measuring several distances and comparing ratios shows that the shadow follows similar triangles.

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What it shows

Light travels in straight lines, so the shadow of an object grows larger as the torch moves closer. Measuring several distances and comparing ratios shows that the shadow follows similar triangles.

The science

Light travels in straight lines. The edge rays from the torch past the top of the object and the edge rays to the wall form two similar triangles. Therefore the shadow height divided by the object height equals the distance from the torch to the wall divided by the distance from the torch to the object.

Materials

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

  • A torch or phone light
  • A small steel tumbler or a cardboard figure 10 cm tall
  • A plain wall
  • A metre ruler or a measuring tape
  • Chalk or masking tape
  • A notebook
  • A calculator

Safety

For this project: Do the activity in a dim room with no stumbling hazards. Do not shine the light into anyone’s eyes.

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. Fix the torch at a steady height, level with the middle of the object, and place the wall 150 cm from the torch.

  2. Place the object 100 cm from the torch and measure the shadow height on the wall in cm.

  3. Move the object to 80, 60, 40 and 20 cm from the torch and measure the shadow each time.

  4. Record the distance and the shadow height in a table.

  5. Calculate the predicted height using the formula and compare it with the measured height.

  6. Draw a graph of shadow height against the object distance.

  7. Explain why the shadow gets blurry at its edges.

What you should see

The shadow grows as the object nears the torch, and the measured heights match the calculated ones within about 1 cm. The graph is a smooth curve rising steeply near the torch.

Viva questions

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

1Why do shadows have the shape of the object?

Light travels straight and is blocked.

2What are similar triangles?

Triangles of the same shape with equal angles and proportional sides.

3Why is the edge of the shadow blurred?

The torch is not a point source, so there is a partial shadow.

4What happens with the sun’s shadows?

They are almost the same size as the object because the sun is very far.

Free ebook: Viva Questions for Science Projects

Take it further

Use the method to find the height of a tall pole from its shadow length and a metre stick.

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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