Table of Contents
Refraction Experiment: Pencil in Water, Measured
A refraction experiment pencil water demonstration with real numbers: the coin that reappears, apparent depth, and measuring n = 1.33 with a protractor.
A refraction experiment pencil water demonstration takes ten seconds: stand a pencil in a glass and look from the side. Everyone has seen it; almost nobody has measured it. This guide starts with that party trick, moves to a coin that reappears from behind the rim of a cup, and ends with a number: water’s refractive index, 1.33, measured with a torch, a bowl and a printed protractor, to within a couple of per cent. Along the way it corrects an explanation that is almost universal and almost right. Water does not bend light because it is thicker. Cooking oil is less dense and bends light considerably more, and that counterexample is worth the afternoon.
Key Takeaways
- A pencil in water looks broken because light from the submerged part changes direction on leaving the water, and your visual system assumes it travelled in a straight line.
- A coin hidden behind the rim of an empty cup reappears when you pour water in, without anyone moving.
- Apparent depth is real depth divided by the refractive index, so a coin 8 cm down looks about 6 cm down.
- You can measure water’s refractive index as 1.33 with a protractor and a torch beam, which is a genuine physics measurement.
- Density is not the cause. Cooking oil is lighter than water and refracts more strongly.
What You’ll Need
| Item | How much | Where to get it | If you don’t have it |
|---|---|---|---|
| Straight-sided clear glass | 1 | A tumbler or jam jar. Straight sides matter; a curved wine glass adds lens effects | A clear plastic food box |
| Pencil or a straight straw | 1 | n/a | A chopstick, a ruler, a skewer |
| Opaque mug or cup | 1 | n/a | Any cup you cannot see through |
| Coin | 1 | n/a | A button or a bottle cap |
| Semicircular dish, or a round glass bowl | 1 | A clear plastic food container works | A round bowl plus patience |
| Printed protractor | 1 | Print one at full page size | Draw one with a compass |
| Bright torch and black card | 1 each | n/a | Cut a 1 mm slit in the card and tape it over the torch |
| Milk | 1 drop per litre | n/a | Makes the beam path visible in the water. One drop only |
| Cooking oil | 100 mL | Kitchen | The counterexample that kills the density explanation |
| Ruler | 1 | n/a | n/a |
Time: prep 10 min, experiment 30 min, cleanup 5 min Cost: nothing Mess level: low for the glass, medium once oil is involved
Do the Experiment: Pencil, Water and Refraction
Step 1 - Make the pencil look broken, then find the angle that matters
Fill a straight-sided glass two-thirds with water and stand a pencil in it, leaning against the rim. Look from the side, with your eye roughly level with the water surface, then from directly above.
What you should see: From the side at a shallow angle, the pencil looks sharply broken at the surface and the submerged part looks wider and shifted. From directly above, there is no bend at all; the pencil just looks shorter. The break depends on your viewing angle, which is the first clue that this is about the direction light leaves the water, not about the pencil.
Step 2 - Collect a prediction about the hidden coin
Put a coin at the bottom of an opaque mug. Lower your eye and back away until the rim of the mug just hides the coin, then hold your head completely still. Ask: “If I pour water in without touching the coin or the cup, will you be able to see it?” Almost everyone says no.
Step 3 - Pour the water
Have someone else pour water slowly into the mug while you keep your head absolutely still.
What you should see: The coin rises into view from behind the rim. Nothing moved. The light leaving the water surface now bends toward you, so rays that previously went over your head now reach your eye. This is the most convincing single demonstration in the whole topic, and it works every time if you keep still.
Step 4 - Measure apparent depth
Fill a glass to a measured depth, say 8 cm, and put a coin on the bottom. Looking straight down, use a ruler held beside the glass to judge how deep the coin appears to be.
What you should see: About 6 cm, not 8. Apparent depth is real depth divided by the refractive index: 8 ÷ 1.333 = 6.0 cm. Judging it by eye is crude, so expect 5.5 to 6.5 cm, but the direction and rough size of the effect are unmistakable.
Step 5 - Measure the refractive index with a protractor
Stand the semicircular dish on the printed protractor with the flat face along the baseline and the centre of that face at the protractor’s origin. Fill it with water and one drop of milk per litre. In a dark room, aim the slit torch beam at the origin from the air side at 20°, then 40°, then 60° to the normal, and read the angle the beam takes inside the water.
What you should see: The beam bends toward the normal on entering. Expect roughly 14.9° for an incident 20°, 28.8° for 40°, and 40.5° for 60°. Now compute sin(incident) ÷ sin(refracted) for each: 0.342/0.257 = 1.33, 0.643/0.482 = 1.33, 0.866/0.650 = 1.33. The same number three times. That constant is Snell’s law and it is water’s refractive index.
Step 6 - Kill the density explanation with cooking oil
Repeat Step 5 with cooking oil in place of water. Oil’s density is about 0.92 g/cm³, clearly less than water’s 1.00, which you can show by floating oil on water first.
What you should see: The oil bends the beam more, giving a ratio near 1.47 rather than 1.33, despite being less dense. Whatever refraction depends on, it is not density. Ask your kid to say that out loud; it is the moment the explanation they have heard falls over.
What’s Actually Going On When Water Bends Light
Light travels more slowly inside water than in air. The ratio of the two speeds is the refractive index, n, and for water with visible light it is about 1.333, a figure tabulated in the reference formulation published by Allan Harvey, J. S. Gallagher and J. M. H. Levelt Sengers in the Journal of Physical and Chemical Reference Data in 1998. In water, light’s phase speed is about 2.25 × 10⁸ m/s rather than 3.00 × 10⁸.
Now picture a wavefront arriving at the surface at an angle. One edge of the wavefront enters the water and slows down while the other edge is still in air and still going fast. The wavefront pivots, like a line of marchers where one end slows, and the direction of travel changes. Work the geometry through and you get Snell’s law: n₁ sin θ₁ = n₂ sin θ₂, with angles measured from the normal, the line perpendicular to the surface. Going from air into water, the ray bends toward the normal. Coming out, it bends away.
That explains the physics, but the illusion needs one more step, and it is the step most explanations skip. The pencil is not bent. The light is. Your visual system has one deeply built-in assumption: light travels in straight lines, so an object sits wherever the backward extension of the rays entering your eye says it does. Rays from the submerged part of the pencil bend away from the normal as they leave the water, so when your brain traces them back in a straight line, it places that part of the pencil somewhere it is not. The break is a reconstruction error, not a deformation.
The same reconstruction explains everything else here. The coin appears shallower because the rays from it leave the surface at a steeper angle than they arrived with, and your brain’s straight-line back-projection places it higher up: apparent depth = real depth ÷ n, which gives three quarters of the true depth for water. The coin reappears from behind a cup’s rim for the same reason, in the horizontal direction.
Now the correction. The explanation you will hear most often is that water bends light “because it is denser” or “because it is thicker than air”. Density is the wrong variable. Refractive index depends on how strongly a material’s electrons respond to the oscillating electric field of the light wave, which is about electronic structure and polarisability, not about mass per unit volume. The counterexample in Step 6 is decisive: cooking oil, at roughly 0.92 g/cm³, is clearly less dense than water at 1.00, and yet its refractive index of around 1.47 is clearly higher. If density were the cause, oil would bend light less. It bends it more.
One honest note on what the illusion needs. The apparent break is strongest at shallow viewing angles and vanishes when you look straight down, where only apparent depth remains, and a curved-sided glass acts as a lens that adds distortion on top. Research bears on this directly: Björn Andersson and Christina Kärrqvist found in 1983 that many pupils aged 12 to 15 do not reliably treat light as something that travels from object to eye, and Galili and Hazan’s 2000 analysis found that learners’ optics knowledge stays fragmented. Without the ray-to-eye model, no amount of explaining the bend will land.
How to Explain It to Your Kid
Ages 5–8: The water moves the picture, not the pencil
Have them hold the pencil and feel that it is straight while looking at it in the water and seeing it broken. Then do the coin-in-the-cup trick and let them pour. Say the water nudges the light sideways on its way out, so their eyes get the wrong address for where the pencil’s bottom is. Let them lift the pencil out and put it back ten times, because the switching is the whole pleasure.
Ages 9–12: Light bends at the surface, and three quarters is the number
Draw the ray diagram: a ray from the coin, bending as it leaves the water, and the dotted straight-line back-extension that shows where the brain puts it. Then do the apparent-depth measurement and give them the rule: what you see is about three quarters of the true depth in water. Measure a deep glass and a shallow one and check the ratio holds. This is the same bending that makes a pencil look fatter and a drop of water act as a lens.
Ages 13+: Three angles, one constant
Have them run Step 5 at five incident angles rather than three, tabulate sin θ₁ and sin θ₂, and plot one against the other. The graph is a straight line through the origin and its gradient is n. Finding a constant hidden in five separate measurements is what a physical law actually looks like. Then push on: at what angle does light inside the water stop being able to get out at all? That question leads directly to total internal reflection and the 48.6° critical angle.
The question to ask: “If I filled the glass with cooking oil instead of water, would the pencil look more broken or less broken? Say which, and say what that tells you about the ‘water is thicker’ explanation.”
Why Teaching This Early Pays Off for Refraction
Refraction is the gateway to the whole of optics, and what makes it hard is not the algebra. The correct explanation requires holding two ideas at once: light changes direction at a boundary, and your visual system assumes it did not. Children with only the first half can recite Snell’s law and still not say why the pencil looks broken. Children with the second half have a tool that also explains mirages, the flattened sun at sunset, and why spear fishing requires aiming low.
The measurement in Step 5 is worth highlighting separately. It is one of the very few home experiments that yields a dimensionless physical constant you can compare against a published value and find agreement to about two per cent. That experience, of a number you measured matching a number in a reference table, is rare and quietly powerful.
Be honest about the limits of the claim. An afternoon of this does not teach optics, and the pencil trick on its own teaches almost nothing, because it is too familiar to provoke a question. What earns its keep is the coin that reappears without anyone touching it, and the oil that refutes the density story. Both are surprises, and a surprise is what makes an explanation worth listening to.
Before You Start: What Parents Should Know
| Best age | 6 to 12 for the tricks, 11 and up for the protractor measurement |
| Supervision | Light. An adult cuts the torch slit and handles any glass containers |
| Real hazards | None beyond water, oil and glass. Spilled cooking oil on a hard floor is genuinely slippery; wipe it immediately with detergent, not just a cloth. Use plastic containers rather than glass with younger children. Do not pour used cooking oil down the drain; let it cool and bin it or take it to a recycling point |
| Don’t | Don’t use a laser pointer in place of the slit torch. It makes the beam easier to see and puts a collimated beam at a child’s eye height next to a bowl of water that will reflect it in unpredictable directions |
When It Doesn’t Work
- The pencil does not look broken. You are looking from too high an angle, or your glass has curved sides. Get your eye down to just above the water line, and use a straight-sided tumbler.
- The coin does not reappear. Your head moved. The effect depends on your eye staying in exactly the same place while the water rises. Rest your chin on the table, and have someone else do the pouring.
- The torch beam is invisible in the water. Add one drop of milk per litre and no more. Two drops scatters so much that the beam blurs and the angle becomes unreadable.
- Your measured index comes out at 1.5 or 1.2. Check that the beam is hitting the centre of the flat face, exactly over the protractor’s origin, and that you are reading angles from the normal rather than from the surface. Measuring from the wrong reference line is the most common error here by a wide margin.
Take It Further
- Plot sin θ₁ against sin θ₂. Five incident angles, three repeats each, plotted as a straight line whose gradient is n. Then repeat for a strong sugar solution, which should land between water and oil, and see whether your three materials rank in the order you expect.
- Measure the apparent depth of a swimming pool. From the edge, estimate the depth by eye, then compare against the posted depth. The shortfall should be close to the factor 1/1.33, which is exactly why people misjudge shallow water.
What to Watch For Over the Next 3 Months
- Week 4: They notice their own legs looking short and bent in the bath, or a straw displaced in a glass of juice, and say why.
- Month 2: The word “refraction” is used about something that is not a pencil. A fish tank, a puddle, the wobbly air above hot tarmac.
- Month 3: If they ask why the sun looks squashed when it sets, they have reached atmospheric refraction, where the air’s index varies continuously with height. That is the same physics with a gradient instead of a sharp boundary, and it is a good next conversation.
Frequently Asked Questions
Why does a pencil look broken in water?
Because light from the submerged part changes direction as it leaves the water, while your visual system assumes light travels in straight lines. Your brain traces the rays straight back and puts the submerged part where it is not. The pencil is straight; the reconstruction is wrong.
Why does the coin reappear when you add water?
Because the rays from the coin bend away from the normal as they leave the water surface, so rays that would have passed above your eye are redirected into it. Nothing moved; the path the light takes changed.
Does water bend light because it is denser than air?
No, and this is a widespread error. Refractive index depends on how a material’s electrons respond to the light wave, not on mass per unit volume. Cooking oil is less dense than water, about 0.92 against 1.00, yet its refractive index of around 1.47 is higher than water’s 1.333.
How deep does a coin look compared with how deep it is?
About three quarters as deep for near-vertical viewing. Apparent depth is real depth divided by the refractive index, so 8 cm of water makes a coin appear about 6 cm down, which is why pools and rivers are deeper than they look.
About the author
Ricky Flores is the founder of HiWave Makers and an electrical engineer with 15+ years of experience building consumer technology at Apple, Samsung, and Texas Instruments. He writes about how kids learn to build, think, and create in a tech-saturated world. Read more at hiwavemakers.com.
Sources
- Harvey, A. H., Gallagher, J. S., & Levelt Sengers, J. M. H. (1998). “Revised Formulation for the Refractive Index of Water and Steam as a Function of Wavelength, Temperature and Density.” Journal of Physical and Chemical Reference Data, 27(4), 761–774. https://doi.org/10.1063/1.556029
- Georgia State University. “Refraction of Light.” HyperPhysics. https://hyperphysics.gsu.edu/hbase/geoopt/refr.html
- The Physics Classroom. “Total Internal Reflection.” https://www.physicsclassroom.com/class/refrn/Lesson-3/Total-Internal-Reflection
- Andersson, B., & Kärrqvist, C. (1983). “How Swedish pupils, aged 12–15 years, understand light and its properties.” European Journal of Science Education, 5(4), 387–402. https://doi.org/10.1080/0140528830050403
- Galili, I., & Hazan, A. (2000). “Learners’ knowledge in optics: interpretation, structure and analysis.” International Journal of Science Education, 22(1), 57–88. https://doi.org/10.1080/095006900290000
- Smith, J. P. III, diSessa, A. A., & Roschelle, J. (1994). “Misconceptions Reconceived: A Constructivist Analysis of Knowledge in Transition.” Journal of the Learning Sciences, 3(2), 115–163. https://doi.org/10.1207/s15327809jls0302_1
- National Research Council. (2012). A Framework for K-12 Science Education. National Academies Press. https://doi.org/10.17226/13165
