Chapter 2 of 8

All 8 chapters
  1. 1Reflection, readunderstood
  2. 2Refraction, readunderstood
  3. 3Lenses and the eye, readunderstood
  4. 4The colours of light, readunderstood
  5. 5Why things have colour, readunderstood
  6. 6Sound as a wave, readunderstood
  7. 7The speed of sound, readunderstood
  8. 8Pitch, loudness and hearing, readunderstood

S3.9.2 Chapter 2

Refraction

Why does a straight stick look bent in water?

Your guess

Pick one before you read on. It is fine to be wrong.

Your guess

  • You picked A. Read on. At the end, the chapter comes back to your guess.

  • You picked B. Read on. At the end, the chapter comes back to your guess.

  • You picked C. Read on. At the end, the chapter comes back to your guess.

By the end you can

  • Explain why a stick looks bent in water
  • Show how pouring water into a cup makes a hidden coin appear

Amina puts a straight stick into a bowl of water. At the water, the stick looks bent. She lifts it out. It is straight again. What happened?

Light travels at different speeds in different materials. A material that light goes through is a medium. Air, water and glass are three media.

Light is quick in air. It is slower in water and slower still in glass. When a ray goes from air into water, it slows down. If it meets the surface at a slant, it also turns. We call this turning refraction.

Think of a cart rolling from a smooth floor onto sand at a slant. The wheel that reaches the sand first slows down first. The cart turns towards the slow side. A ray of light turns in the same way.

Draw it first

Draw a ray going into water

  1. A pool of water with air above it. A dashed line, labelled normal, stands at right angles to the surface. In the second picture a ray comes down from the upper left to the surface at 45°, labelled 45°. In the third picture the ray carries on into the water at 32° from the normal, labelled 32°. Labels: normal, air, water, 45°, 32°.normalairwater

    1 Draw the water surface and the normal at right angles to it.

  2. A pool of water with air above it. A dashed line, labelled normal, stands at right angles to the surface. In the second picture a ray comes down from the upper left to the surface at 45°, labelled 45°. In the third picture the ray carries on into the water at 32° from the normal, labelled 32°. Labels: normal, air, water, 45°, 32°.normalairwater45°

    2 Draw the ray in the air, 45° from the normal. It points at the surface.

  3. A pool of water with air above it. A dashed line, labelled normal, stands at right angles to the surface. In the second picture a ray comes down from the upper left to the surface at 45°, labelled 45°. In the third picture the ray carries on into the water at 32° from the normal, labelled 32°. Labels: normal, air, water, 45°, 32°.normalairwater45°32°

    3 In the water the ray is closer to the normal. Draw it 32° from the normal. It bends towards the normal.

A ray comes down through air to the surface of water and carries on into the water, bending towards the dashed normal. The angle in the air is 40° and the angle in the water is 29°. Labels: air, water, normal, 40°, 29°.airwaternormal40°29°
From air into water, the ray bends towards the normal. The angle gets smaller.

Coming out of water into air, a ray speeds up. It bends away from the normal. The angle gets bigger.

A ray that goes along the normal does not bend. It slows down but keeps going straight on.

A ray travels up through water to the surface and out into the air, bending away from the dashed normal. The angle in the water is 30° and the angle in the air is 42°. An eye on the right looks back along the ray. A dotted straight line goes on down into the water from the eye. Labels: air, water, normal, 30°, 42°.airwaternormal30°42°
The eye cannot know the ray bent. It traces the light back in a straight line, shown dotted. That is where the thing seems to be.

Now you can explain the stick. Light from the part under water bends as it comes out. Your eye traces it straight back, to a higher place. The part under water seems raised, so the stick looks bent.

A stick goes down through the surface of water. Above the water it is straight. Under the water it looks bent upwards. A dashed line shows where the stick really is. Labels: air, water, looks, is.airwaterlooksis
The solid line is what you see. The dashed line is where the stick really is.

See it three ways

As a picture

A table with two columns, in air and in water. 0° in air, 0° in water. 20° in air, 15° in water. 40° in air, 29° in water. 60° in air, 41° in water.in airin water0°0°20°15°40°29°60°41°

In words

The angle in the water is smaller than the angle in the air. At 0° there is no bend. A bigger angle in the air makes a bigger bend.

In symbols

air to water: the angle gets smaller. Water to air: the angle gets bigger.

Because the eye traces light straight back, water always looks shallower than it is. Looking straight down, it looks about 3/4 as deep.

A table with two columns, real depth and looks about. The real depth is 12 cm. The depth it looks is a question mark. Labels: real depth, looks about, 12 cm, ? cm.real depthlooks about12 cm? cm
A cup of water that is 12 cm deep. About how deep does it look from straight above?

Worked example

A cup holds water 12 cm deep. About how deep does it look from straight above?

  1. Water looks about 3 quarters as deep as it is.
  2. One quarter of 12 cm is 12 ÷ 4 = 3 cm.
  3. Three quarters is 3 × 3 = 9 cm.

Answer: 9 cm

A cup seen from the side with a coin on its bottom, and an eye beyond the rim. A dotted line from the coin to the eye is blocked by the wall of the cup, so the eye cannot see the coin. Labels: coin, eye.coineye
With no water, the cup wall blocks the straight line from the coin to the eye.

Now fill the cup. Light from the coin bends as it leaves the water. It now goes over the rim and into the eye. The eye traces it back, and the coin seems to float up.

Try it

Make a coin appear

You need: an opaque cup, such as a clay or metal cup, a small flat thing, such as a coin, a button or a flat stone, water in a jug or bottle.

Be safe: Pour slowly and mop up spills so no one slips. Do not look into the Sun through water or glass.

  1. Put the coin on the bottom of the empty cup.
  2. Sit with your eye low. Move back until the rim just hides the coin.
  3. Keep your head still. Ask a friend to pour water slowly into the cup.
  4. Watch the coin. Do not move your head.

What you will see: The coin comes into view as the water rises. The coin has not moved. The light from it now bends as it leaves the water, and it reaches your eye.

If you cannot try it, this is what happens.
The same cup, now with water. A ray goes from the coin up to the surface and bends towards the eye. A dotted line goes back from the eye to a point higher than the coin, labelled looks here. Labels: coin, eye, water, looks here.coineyewaterlooks here

A wrong idea many people have

Water bends the stick, or it makes things move.

Why it feels right: You can see the bend, and the stick looks different in water.

The test that breaks it: Pull the stick out. It is straight. Put it back and move your head until you look down from straight above it. The bend shrinks and then it is gone.

What is true: Only the light bends. Your eye traces the bent light back in a straight line. So the object seems to be in a different place.

Key words

medium
a material that light travels through, such as air, water or glass.
refraction
the bending of light when it goes from one medium into another.

Back to your guess

The answer is A: Light bends as it leaves the water, so our eyes are fooled.

The stick stays straight. Light from the part under water bends as it comes out into the air. Our eyes trace it back in a straight line, so the stick seems to bend.

Check yourself

Try each one before you look. A wrong answer tells you where to go next.

  1. The water in a well is 8 m deep. About how deep does it look from straight above?

    Tap your answer.

    1. Not this one. The light bends, so the water does not look its true depth. Go to S3.9.2. Try another.

    2. Not this one. Water looks shallower, not deeper. The eye traces light back to a higher place. Go to S3.9.2. Try another.

    3. Not this one. That is half. Water looks about 3 quarters as deep. Go to S3.9.2. Try another.

    4. Yes, that is right. Water looks about 3 quarters as deep. 8 ÷ 4 = 2, and 2 × 3 = 6 m.

    See the answer

    6 m

    Water looks about 3 quarters as deep. 8 ÷ 4 = 2, and 2 × 3 = 6 m.

    • If you chose A: The light bends, so the water does not look its true depth. Go to S3.9.2.
    • If you chose B: Water looks shallower, not deeper. The eye traces light back to a higher place. Go to S3.9.2.
    • If you chose C: That is half. Water looks about 3 quarters as deep. Go to S3.9.2.

  2. A ray in air meets the surface of water at 30° from the normal. Which way does it bend as it goes into the water?

    A ray comes down through air to the surface of water. A dashed normal stands at right angles to the surface. The ray is drawn only as far as the surface. Labels: air, water, normal.normalairwater
    Tap your answer.

    1. Not this one. That is what happens coming out of water. Going in, the light slows down and turns towards the normal. Go to S3.9.2. Try another.

    2. Yes, that is right. The light slows down in water. A ray at a slant turns towards the normal, so the angle in the water is smaller.

    3. Not this one. Only a ray along the normal goes straight on. A ray at a slant bends when it changes medium. Go to S3.9.2. Try another.

    See the answer

    Towards the normal.

    The light slows down in water. A ray at a slant turns towards the normal, so the angle in the water is smaller.

    • If you chose A: That is what happens coming out of water. Going in, the light slows down and turns towards the normal. Go to S3.9.2.
    • If you chose C: Only a ray along the normal goes straight on. A ray at a slant bends when it changes medium. Go to S3.9.2.

  3. Why does a straight stick look bent where it goes into water?

    Tap your answer.

    1. Not this one. The stick is still straight when you pull it out. Only the light bends. Go to S3.9.2. Try another.

    2. Not this one. The stick has not changed. Light from it bends, and your eye is fooled about where it is. Go to S3.9.2. Try another.

    3. Yes, that is right. Your eye traces the bent light back in a straight line. That line leads to a higher place, so the part under water seems raised.

    See the answer

    Light from the part under water bends as it comes out, so the part seems higher.

    Your eye traces the bent light back in a straight line. That line leads to a higher place, so the part under water seems raised.

    • If you chose A: The stick is still straight when you pull it out. Only the light bends. Go to S3.9.2.
    • If you chose B: The stick has not changed. Light from it bends, and your eye is fooled about where it is. Go to S3.9.2.

  4. Mei cannot see a coin at the bottom of an empty cup. She pours in water, and now she can see it. Why?

    Tap your answer.

    1. Yes, that is right. Without water the rim blocks the straight line. The bent ray passes over the rim. The eye traces it back to a place higher than the coin.

    2. Not this one. The coin has not moved. It only seems higher because light bends. Go to S3.9.2. Try another.

    3. Not this one. Water gives off no light. It only bends the light that comes from the coin. Go to S3.9.2. Try another.

    See the answer

    Light from the coin bends as it leaves the water, and now reaches her eye over the rim.

    Without water the rim blocks the straight line. The bent ray passes over the rim. The eye traces it back to a place higher than the coin.

    • If you chose B: The coin has not moved. It only seems higher because light bends. Go to S3.9.2.
    • If you chose C: Water gives off no light. It only bends the light that comes from the coin. Go to S3.9.2.

  5. A ray goes from water into air at a slant. What happens to its speed and direction?

    Tap your answer.

    1. Not this one. That is going into water. Coming out, the light speeds up and bends away. Go to S3.9.2. Try another.

    2. Yes, that is right. Light is quicker in air than in water. A ray that speeds up turns away from the normal.

    3. Not this one. Light that speeds up turns away from the normal. Light that slows turns towards it. Go to S3.9.2. Try another.

    See the answer

    It speeds up and bends away from the normal.

    Light is quicker in air than in water. A ray that speeds up turns away from the normal.

    • If you chose A: That is going into water. Coming out, the light speeds up and bends away. Go to S3.9.2.
    • If you chose C: Light that speeds up turns away from the normal. Light that slows turns towards it. Go to S3.9.2.

  6. From an earlier chapter

    Review: a ray hits a flat mirror at 35° from the normal. At what angle from the normal does it leave?

    Tap your answer.

    1. Not this one. You measured from the mirror. Measure both angles from the normal. Go to S3.9.1. Try another.

    2. Not this one. You added the two angles together. The angle of reflection simply equals the angle of incidence. Go to S3.9.1. Try another.

    3. Yes, that is right. The angle of reflection equals the angle of incidence, so the ray leaves at 35°.

    See the answer

    35°

    The angle of reflection equals the angle of incidence, so the ray leaves at 35°.

    • If you chose A: You measured from the mirror. Measure both angles from the normal. Go to S3.9.1.
    • If you chose B: You added the two angles together. The angle of reflection simply equals the angle of incidence. Go to S3.9.1.

Keep it

Copy this into your exercise book.

Light slows down in water. A ray going in bends towards the normal. A ray coming out bends away. Eyes trace light straight back, so water looks shallower and a stick looks bent.

Draw: A water surface with a dashed normal. A ray in air at 45°. A ray in water at 32°, closer to the normal.

Reading with a child? A short page for the adult: what this chapter teaches and three questions to ask.

No internet tomorrow? Save the whole book as one file (720 KB). It opens on any phone.