Chapter 1 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

S3.9.1 Chapter 1

Reflection

When light hits a mirror, which way does it go?

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

  • Show that light leaves a mirror at the same angle it arrives
  • Draw rays reflecting from a flat mirror with a ruler

Mei holds a small mirror. Her friend Ravi stands to one side. Mei sees Ravi in the mirror. The light from Ravi has bounced off the mirror into her eyes.

When light bounces off a surface, we call it reflection. A flat mirror is very smooth, so it reflects light in a neat and certain way.

To say which way a ray goes, we need a line to measure from. Draw a dashed line at right angles to the mirror. This line is called the normal.

The ray that comes in makes an angle with the normal. This is the angle of incidence. The ray that leaves makes an angle with the normal too. This is the angle of reflection.

Here is the rule. The angle of reflection always equals the angle of incidence. A ray that comes in at 35° leaves at 35°, on the other side of the normal.

Draw it first

Draw a reflection

  1. A flat mirror along the bottom, labelled mirror, with a dashed line standing up from it, labelled normal. In the second picture a ray comes down to the mirror from the upper left, labelled in 35°. In the third picture a ray leaves to the upper right, labelled out 35°. Labels: mirror, normal, in 35°, out 35°.mirrornormal

    1 Draw the mirror as a straight line. Mark a point on it. Draw the normal from that point with a ruler, at right angles.

  2. A flat mirror along the bottom, labelled mirror, with a dashed line standing up from it, labelled normal. In the second picture a ray comes down to the mirror from the upper left, labelled in 35°. In the third picture a ray leaves to the upper right, labelled out 35°. Labels: mirror, normal, in 35°, out 35°.mirrornormalin 35°

    2 Draw the ray that comes in, 35° from the normal. Put an arrow on it pointing at the mirror.

  3. A flat mirror along the bottom, labelled mirror, with a dashed line standing up from it, labelled normal. In the second picture a ray comes down to the mirror from the upper left, labelled in 35°. In the third picture a ray leaves to the upper right, labelled out 35°. Labels: mirror, normal, in 35°, out 35°.mirrornormalin 35°out 35°

    3 Draw the ray that leaves on the other side of the normal, also 35° from it. The arrow points away.

A flat mirror with a dashed normal, labelled mirror and normal. Two rays come in from the left, one at 25° and one at 50° from the normal. Two rays leave to the right at the same two angles. Labels: mirror, normal, 25°, 50°.mirrornormal25°25°50°50°
Two rays hit the same spot. Each one leaves at the angle it came in. A ray that arrives lower leaves lower.

Always measure from the normal. Do not measure from the mirror. The mirror is a flat surface, but the angle rule is about the normal.

A ray that travels along the normal, at 0°, hits the mirror straight on. It leaves at 0° too. It goes straight back the way it came.

A rough surface is covered with tiny bumps. Each bump faces a different way. Each ray still obeys the rule, but the bumps tilt, so the rays leave in many directions.

Two surfaces. At the top is a smooth flat surface, labelled smooth. Three parallel rays hit it and leave side by side in the same direction. Below is a bumpy surface, labelled rough. Three parallel rays hit three little faces tilted different ways and leave in three different directions. Labels: smooth, rough.smoothrough
A smooth surface sends light one way, so you see an image. A rough surface scatters light, so you see no image.

See it three ways

As a picture

A table with two columns, angle in and angle out. 20° in, 20° out. 35° in, 35° out. 50° in, 50° out. 65° in, 65° out.angle inangle out20°20°35°35°50°50°65°65°

In words

Every row of the table has the same number twice. The angle that leaves is always the angle that arrived.

In symbols

angle of reflection = angle of incidence.

Sometimes you are told the angle between the ray and the mirror. That is not the angle of incidence. The normal and the mirror meet at 90°, so you take the angle away from 90°.

A flat mirror with a dashed normal, labelled mirror and normal. A ray comes in from the left and makes 25° with the mirror, marked by a small arc. A ray leaves to the right. The angle between the normal and the ray that leaves is marked with a question mark. Labels: mirror, normal, 25°, ?.mirrornormal25°?
The ray makes 25° with the mirror. What angle does it make with the normal?

Worked example

A ray meets a flat mirror and makes 25° with the mirror. What is the angle of reflection?

  1. The normal is at 90° to the mirror.
  2. The angle of incidence = 90° − 25° = 65°.
  3. The angle of reflection equals the angle of incidence, so it is 65°.

Answer: 65°

Try it

Find the angle with a pencil

You need: a small flat mirror, a sheet of paper, a pencil standing in a lump of clay or between two stones, a ruler, or a stick with centimetres marked on it.

Be safe: A mirror can break. Keep it away from the edge of the table. If it breaks, leave the pieces and ask an adult to clear them.

  1. Draw a straight line on the paper. Stand the mirror upright on it, held by stones.
  2. Mark a point in the middle of the line. Use the corner of the paper to draw the normal from it.
  3. Stand the pencil on the paper, to one side of the normal, 10 cm from the point.
  4. Lay the ruler on the other side of the normal, with its 0 end on the point. Put your eye low at the 10 cm end and look along the ruler.
  5. Turn the ruler a little at a time. Stop when you see the pencil in the mirror, right at the point. Draw a line along the ruler.
  6. Measure straight across from the pencil to the normal, and from the 10 cm mark to the normal. Compare them.

What you will see: The two distances come out about the same. The pencil and your eye sit at equal angles from the normal. That is the rule: the angle in equals the angle out.

If you cannot try it, this is what happens.
A flat mirror with a dashed normal. A ray goes from a pencil at the left to the mirror at 40° from the normal, and then to an eye at the right, also 40° from the normal. Labels: mirror, normal, pencil, eye, 40°.mirrornormalpencileye40°40°

A wrong idea many people have

Light always bounces straight back off a mirror.

Why it feels right: When you stand in front of a mirror, you see your own face. That looks like light going straight back.

The test that breaks it: Stand in front of a wall mirror. Ask a friend to stand a few steps to your side. You can see your friend in the mirror, and your friend can see you.

What is true: Light leaves at the same slant it came in. Light from your friend came from the side, so it left towards you at the same slant.

Key words

reflection
light bouncing off a surface.
normal
a line drawn at right angles to the mirror, to measure angles from.
angle of incidence
the angle between the ray that comes in and the normal.
angle of reflection
the angle between the ray that leaves and the normal.

Back to your guess

The answer is A: Away at the same slant it came in, on the other side of the upright line.

The light leaves at the same slant it came in, on the other side of the upright line. It is not random, and it does not come straight back unless it arrived straight on.

Check yourself

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

  1. A ray hits a flat mirror at 30° from the normal. At what angle from the normal does it leave?

    A flat mirror with a dashed normal, labelled mirror and normal. One ray comes in from the left and meets the mirror. Nothing leaves yet. Labels: mirror, normal.mirrornormal
    Tap your answer.

    1. Not this one. You measured from the mirror, 90° − 30°. Measure both angles from the normal. Go to S3.9.1. Try another.

    2. Yes, that is right. The two angles are equal. A ray that comes in at 30° leaves at 30°.

    3. Not this one. You took the angle away from 180°. The angle of reflection is the same as the angle of incidence, so just copy it. Go to S3.9.1. Try another.

    4. Not this one. Only a ray along the normal goes straight back. This ray came in at a slant, so it leaves at a slant. Go to S3.9.1. Try another.

    See the answer

    30°

    The two angles are equal. A ray that comes in at 30° leaves at 30°.

    • If you chose A: You measured from the mirror, 90° − 30°. Measure both angles from the normal. Go to S3.9.1.
    • If you chose C: You took the angle away from 180°. The angle of reflection is the same as the angle of incidence, so just copy it. Go to S3.9.1.
    • If you chose D: Only a ray along the normal goes straight back. This ray came in at a slant, so it leaves at a slant. Go to S3.9.1.

  2. A ray makes 20° with the surface of a flat mirror. What is the angle of incidence, measured from the normal?

    A flat mirror with a dashed normal, labelled mirror and normal. A ray comes in from the left and makes 20° with the mirror, marked by a small arc. Labels: mirror, normal, 20°.mirrornormal20°
    Tap your answer.

    1. Not this one. That is the angle with the mirror. The angle of incidence is measured from the normal, which is at 90° to the mirror. Go to S3.9.1. Try another.

    2. Not this one. You took the angle away from 180°. The normal and the mirror make 90°, so use 90°. Go to S3.9.1. Try another.

    3. Yes, that is right. The normal is at 90° to the mirror. The angle from the normal is 90° − 20° = 70°.

    4. Not this one. You added the angle to 90°. Take it away from 90° instead. Go to S3.9.1. Try another.

    See the answer

    70°

    The normal is at 90° to the mirror. The angle from the normal is 90° − 20° = 70°.

    • If you chose A: That is the angle with the mirror. The angle of incidence is measured from the normal, which is at 90° to the mirror. Go to S3.9.1.
    • If you chose B: You took the angle away from 180°. The normal and the mirror make 90°, so use 90°. Go to S3.9.1.
    • If you chose D: You added the angle to 90°. Take it away from 90° instead. Go to S3.9.1.

  3. You draw a ray reflecting from a flat mirror with a ruler. Which step must you do first?

    Tap your answer.

    1. Yes, that is right. The two angles are measured from the normal, so it comes first. Then draw the ray that comes in, and then the ray that leaves at the same angle.

    2. Not this one. You cannot place the ray that leaves until you know the angle in. Start with the mirror and the normal. Go to S3.9.1. Try another.

    3. Not this one. Angles are measured from the normal, not from the mirror. Draw the normal first. Go to S3.9.1. Try another.

    See the answer

    Draw the normal at right angles to the mirror.

    The two angles are measured from the normal, so it comes first. Then draw the ray that comes in, and then the ray that leaves at the same angle.

    • If you chose B: You cannot place the ray that leaves until you know the angle in. Start with the mirror and the normal. Go to S3.9.1.
    • If you chose C: Angles are measured from the normal, not from the mirror. Draw the normal first. Go to S3.9.1.

  4. Why can you see your face in a smooth mirror, but not in a rough wall?

    Tap your answer.

    1. Not this one. You can see a wall, so light must bounce off it into your eyes. Go to S2.6.7. Try another.

    2. Yes, that is right. Each ray from your face follows the rule on a smooth surface, so the rays stay in order. A rough wall scatters them, so no picture forms.

    3. Not this one. A mirror only bounces light. With no light to bounce, it shows nothing. Go to S2.6.7. Try another.

    See the answer

    A smooth mirror sends light from your face one way, so it makes a clear picture.

    Each ray from your face follows the rule on a smooth surface, so the rays stay in order. A rough wall scatters them, so no picture forms.

    • If you chose A: You can see a wall, so light must bounce off it into your eyes. Go to S2.6.7.
    • If you chose C: A mirror only bounces light. With no light to bounce, it shows nothing. Go to S2.6.7.

  5. Tariq shines light at a mirror at 50° from the normal. He turns his torch so the angle becomes 20° from the normal. What happens to the angle at which the light leaves?

    Tap your answer.

    1. Not this one. The light leaves at the angle it came in. When the angle in changes, the angle out changes too. Go to S3.9.1. Try another.

    2. Not this one. You took one angle away from the other. The angle out simply matches the new angle in. Go to S3.9.1. Try another.

    3. Yes, that is right. The angle out equals the angle in. The new angle in is 20°, so the new angle out is 20°.

    See the answer

    It changes to 20°.

    The angle out equals the angle in. The new angle in is 20°, so the new angle out is 20°.

    • If you chose A: The light leaves at the angle it came in. When the angle in changes, the angle out changes too. Go to S3.9.1.
    • If you chose B: You took one angle away from the other. The angle out simply matches the new angle in. Go to S3.9.1.

Keep it

Copy this into your exercise book.

The normal is a line at right angles to the mirror. The angle of reflection equals the angle of incidence, both from the normal. A smooth surface reflects one way. A rough one scatters light.

Draw: A mirror line with a dashed normal. A ray in at 30° and a ray out at 30°, with arrows.

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.