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GCSE Physics · GCSEChapter 18 · Reflection, refraction and lenses
GCSE · Chapter 18

Reflection, refraction and lenses

By the end of this chapter you will be able to

  • Use the law of reflection and describe the image in a plane mirror
  • Explain refraction using the speed of light in the two materials
  • Draw or describe ray diagrams for a converging lens, and say whether the image is real or virtual
  • [H] Explain total internal reflection and the critical angle

You should already know

  • Waves: wave speed, wavelength and refraction (Chapter 17)
  • The electromagnetic spectrum (Chapter 19, later)

Where this leads

  • The electromagnetic spectrum (Chapter 19)
  • Magnetism and electromagnetism (Chapter 20)

GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: State the law of reflection, and describe images in plane mirrors, Describe refraction at a boundary: towards the normal when entering a denser medium, away when leaving, [H] Describe the critical angle and total internal reflection, for example in optical fibres, Describe converging and diverging lenses, the principal focus and focal length, and construct ray diagrams, Describe real and virtual images, and determine a focal length from a ray diagram, Describe the required practicals: refraction in a glass block and the focal length of a converging lens.

Exercise P  Do you remember?

1
FWhat is 3 + 3 + 4? Write the number.
2
FWhat is a right angle, in degrees? Write the number.
3
FWhat is the speed of light in a vacuum, approximately, in m/s? Write the number as 3 x 10 to the power 8.
4
FWhich way does a wave bend when it slows down? Write towards or away from the normal.
5
FWhat is 1/4 + 1/4? Write the answer as a fraction.
18.1

Reflection and plane mirrors

GCSE
State the law of reflection, and describe images in plane mirrors
Video lesson: Reflection and plane mirrorsComing soon
Context. Ruby looks into a bathroom mirror. Her image looks as far behind the glass as she is in front of it. “Why?” she asks. The answer is the law of reflection, which decides where light goes after it bounces off a surface.

When light reflects from a smooth flat surface, the angle of incidence (between the incoming ray and the normal, the line at right angles to the surface) is equal to the angle of reflection. The incident ray, the reflected ray and the normal all lie in one plane.

In a plane mirror, the image is virtual (it cannot be projected on a screen), the same size as the object, the right way round (upright), and as far behind the mirror as the object is in front.

irnormalangle of incidence (i) = angle of reflection (r)
The law of reflection: angle of incidence = angle of reflection
plane mirror: the image is as far behind the mirror as the object is in frontobjectimage
A plane mirror: the image is as far behind the mirror as the object is in front

Key ideas

  • Law of reflection: angle of incidence = angle of reflection.
  • Normal: the line at right angles to the surface.
  • Plane mirror image: virtual, upright, same size, same distance behind the mirror.
  • The image cannot be caught on a screen.
Worked example 18.1.1
An object is 2 cm in front of a plane mirror. How far is the image from the object? Write the number of cm.

Method. The image is the same distance behind the mirror.

  1. Object to mirror. The object is 2 cm from the mirror.
    2 cm
  2. Image to mirror. The image is 2 cm behind the mirror.
    2 cm
  3. Total. Object to image = 2 + 2 = 4 cm.
    2 + 2 = 4
  4. Write the answer.
    4 cm

Check. ✓

Worked example 18.1.2
A ray hits a plane mirror at an angle of incidence of 35 degrees. What is the angle of reflection? Write the number of degrees.

Method. The angle of reflection equals the angle of incidence.

  1. Look. The ray arrives at 35 degrees to the normal.
    35 degrees
  2. Recall. The law of reflection: angle of reflection = angle of incidence = 35 degrees.
    35
  3. Write the answer.
    35 degrees

Check. ✓

Worked example 18.1.3
A pupil stands 3 m in front of a plane mirror. How far is she from her image? Write the number of metres.

Method. The image is as far behind the mirror as she is in front.

  1. Her distance. She is 3 m from the mirror.
    3 m
  2. Image distance. The image is 3 m behind the mirror.
    3 m
  3. Total. Distance from her to the image = 3 + 3 = 6 m.
    3 + 3 = 6
  4. Write the answer.
    6 m

Check. ✓

Watch out

Watch out: the angles are measured from the normal, not from the mirror surface. A ray at 30 degrees to the surface has an angle of incidence of 60 degrees.

Exam tip

Exam tip. Draw the normal first, as a dashed line at right angles to the surface. Measure both angles from it.

Exercise 18A  Reflection and plane mirrors

1
FWhat is the name of the line at right angles to a mirror at the point of incidence? Write the word.
2
FA ray has an angle of incidence of 25 degrees. What is the angle of reflection? Write the number of degrees.
3
FA ray arrives at 40 degrees to the normal. What is the angle of reflection? Write the number of degrees.
4
FIs the image in a plane mirror upright or inverted? Write the word.
5
FIs the image in a plane mirror real or virtual? Write the word.
6
PSA pupil stands 1.5 m in front of a plane mirror. How far is she from her image? Write the number of metres.
7
PSA plane mirror is tilted by 10 degrees, and the incoming ray stays the same. By how many degrees does the reflected ray turn? Write the number of degrees.
8
RExplain why you can see your image in a flat mirror, in one sentence. Accept any sentence that says light from you reflects off the mirror into your eyes, as the law of reflection describes.
9
RA pupil says “the image in a mirror is the same distance behind the mirror as the object is in front.” Is the pupil right? Write yes or no.
10
RA pupil says the image in a plane mirror is smaller than the object. Explain why this is wrong, in one sentence. Accept any sentence that says a plane mirror image is the same size as the object.
11
PSA ray of light is incident at 20 degrees on a plane mirror. What is the angle between the incident ray and the mirror surface? Write the number of degrees.
12
FName the device in which a pupil would use a ray box to trace refraction through a glass block. Write the word.
18.2

Refraction at a boundary

GCSE
Describe refraction at a boundary: towards the normal when entering a denser medium, away when leaving
Video lesson: Refraction at a boundaryComing soon
Context. A straw in a glass of water looks bent at the surface. The ray of light from the straw changes direction as it leaves the water. This is refraction: light changes direction when its speed changes at a boundary.

Light travels slower in denser materials such as glass and water than in air. When light enters a denser material at an angle, it slows down and bends towards the normal. When it leaves the denser material, it speeds up and bends away from the normal. A ray along the normal is not bent. The frequency of the light does not change at the boundary.

ray bends towards the normal entering the glass, and away from it leavingincident ray
Refraction through a glass block: towards the normal on entry, away from it on exit

Key ideas

  • Light slows down in a denser material, and bends towards the normal.
  • Light speeds up when leaving a denser material, and bends away from the normal.
  • A ray along the normal is not bent.
  • The frequency does not change at a boundary.
Worked example 18.2.1
A ray enters a glass block. Does it bend towards or away from the normal on entry? Write the word.

Method. Glass is denser than air, so light slows down.

  1. Look. Light slows down when it enters denser glass.
    slows down
  2. Decide. A slowing wave bends towards the normal.
    towards
  3. Write the answer.
    towards

Check. ✓

Worked example 18.2.2
The same ray leaves the glass block into air. Does it bend towards or away from the normal? Write the word.

Method. Light speeds up when it leaves glass.

  1. Look. Light speeds up leaving the glass into air.
    speeds up
  2. Decide. So it bends away from the normal.
    away
  3. Write the answer.
    away

Check. ✓

Worked example 18.2.3
A ray enters a block of glass from air. Does its speed increase or decrease? Write the word.

Method. Glass is denser than air.

  1. Look. Light moves more slowly in denser material such as glass.
    slower
  2. Decide. So the speed decreases on entering the glass.
    decrease
  3. Write the answer.
    decrease

Check. ✓

Watch out

Watch out: refraction bends light towards the normal when it slows down, not when it is more dense. The rule is about the change of speed.

Exam tip

Exam tip. In the practical, trace the ray through the block with pencil marks at each point, and draw the normal at each surface.

Exercise 18B  Refraction

1
FWhat is refraction? Write the word.
2
FWhen light enters glass from air, does it speed up or slow down? Write the word.
3
FWhen light enters glass at an angle, does it bend towards or away from the normal? Write the word.
4
FA ray leaves a glass block at an angle. Does it bend towards or away from the normal? Write the word.
5
FA ray along the normal enters a glass block. Is it bent? Write yes or no.
6
FDoes the frequency of light change when it enters glass? Write yes or no.
7
FIn the glass block practical, what is drawn at each surface to help measure the angles? Write the word.
8
RA pupil says “light speeds up when it enters water.” Is the pupil right? Write yes or no.
9
RExplain in one sentence why a straw in a glass of water looks bent. Accept any sentence that says light from the straw refracts at the surface, so the image looks displaced.
10
PSA ray enters a material and bends towards the normal. Is the material denser or less dense than the material it came from? Write denser or less dense.
11
RExplain why light bends at a boundary, in one sentence. Accept any sentence that says the speed of light changes in the new material.
12
FRefraction happens at a boundary. Name the quantity that changes at the boundary, apart from direction. Write the word.
13
PSA ray goes from air into water and bends towards the normal. What is the change in speed? Write the word: increase or decrease.
18.3

[H] Critical angle and total internal reflection

GCSE
[H] Describe the critical angle and total internal reflection, for example in optical fibres
Video lesson: [H] Critical angle and total internal reflectionComing soon

[H] Higher tier only. When light travels from a denser material to a less dense one (for example from glass to air), there is an angle of incidence, the critical angle, at which the refracted ray grazes the surface. For a larger angle of incidence, the light is totally internally reflected: none of it leaves the denser material. For glass the critical angle is about 42 degrees.

Total internal reflection is used in optical fibres: light is kept inside the fibre by repeated total internal reflection, so it can carry signals (for example in telecommunications and medical endoscopes). The fibre is thin and the light stays inside its core.

Key ideas

  • [H] Critical angle: the angle of incidence (in the denser material) at which the refracted ray grazes the surface.
  • [H] Above the critical angle, total internal reflection happens.
  • [H] Optical fibres use total internal reflection to carry light signals.
  • [H] For glass to air, the critical angle is about 42 degrees.
Worked example 18.3.1
[H] For glass, the critical angle is about 42 degrees. A ray in glass hits the boundary at 50 degrees. What happens to the ray? Write total internal reflection or refraction.

Method. Compare the angle with the critical angle.

  1. Compare. 50 degrees is greater than the critical angle of 42 degrees.
    50 > 42
  2. Decide. So the ray is totally internally reflected.
    total internal reflection
  3. Write the answer.
    total internal reflection

Check. ✓

Worked example 18.3.2
[H] What is the approximate critical angle for light going from glass to air? Write the number of degrees.

Method. Recall the value for glass.

  1. Recall. For glass to air the critical angle is about 42 degrees.
    42
  2. Check. Any angle of incidence above this in the glass gives total internal reflection.
    > 42
  3. Write the answer.
    42 degrees

Check. ✓

Worked example 18.3.3
[H] Why does light stay inside an optical fibre? Write the reason in one sentence. Accept any sentence that says it undergoes total internal reflection at the boundary of the core.

Method. Think about the boundary inside the fibre.

  1. Boundary. The light meets the wall of the core at a large angle.
    large angle
  2. Reflect. Above the critical angle it is totally internally reflected, so it stays in the core.
    total internal reflection
  3. Write the answer.
    Accept any sentence that says it undergoes total internal reflection at the boundary of the core.

Check. ✓

Watch out

Watch out: [H] total internal reflection needs the light to travel from the denser material to the less dense one, and the angle must be larger than the critical angle.

Exam tip

Exam tip. [H] Name the critical angle and say that total internal reflection happens above it. Give the fibre example for a second mark.

Exercise 18C  [H] Critical angle and fibres

1
F[H] What is the name of the angle above which total internal reflection happens? Write the phrase.
2
F[H] Which device uses total internal reflection to carry signals? Write the name.
3
PS[H] Is total internal reflection possible when light goes from air into glass? Write yes or no.
4
PS[H] For glass to air, the critical angle is about 42 degrees. Light hits the boundary at 30 degrees. Does total internal reflection occur? Write yes or no.
5
R[H] Explain why optical fibres lose less signal than wires, in one sentence. Accept any sentence that says light is kept inside the fibre by total internal reflection, with little loss.
6
PS[H] For glass, the critical angle is about 42 degrees. A ray in glass meets the boundary at 40 degrees. Does total internal reflection occur? Write yes or no.
7
F[H] Name the process that keeps light inside the core of an optical fibre. Write the phrase.
8
R[H] Give the two conditions needed for total internal reflection, in one sentence. Accept any sentence that says the light goes from denser to less dense, and the angle is greater than the critical angle.
9
F[H] Give one use of total internal reflection besides optical fibres. Write one word.
10
RExplain why total internal reflection needs the light to be in the denser material, in one sentence. Accept any sentence that says the light must be going from denser to less dense for the angle to exceed the critical angle.
18.4

Lenses, focal length and ray diagrams

GCSE
Describe converging and diverging lenses, the principal focus and focal length, and construct ray diagrams, Describe real and virtual images, and determine a focal length from a ray diagram
Video lesson: Lenses, focal length and ray diagramsComing soon
Context. A magnifying glass makes a small text look bigger. A projector puts a sharp picture on a screen. Both use lenses, but they form different images. Ray diagrams show us where the image is and what it looks like.

A converging (convex) lens is thicker in the middle. Parallel rays from a distant object are brought together at the principal focus, F. The distance from the centre of the lens to F is the focal length. A diverging (concave) lens is thinner in the middle and spreads parallel rays out, as if they came from a point on the same side.

Three rays help us draw the image for a converging lens: (1) a ray parallel to the axis is refracted through F; (2) a ray through the centre goes straight on; (3) a ray through the near F emerges parallel to the axis. When the object is outside F, the image is real (it can be projected onto a screen), inverted and may be bigger or smaller. When the object is inside F, the image is virtual (it cannot be projected), upright and magnified.

FFobjectimageobject 12 cm away, focal length 4 cm (drawn to scale)
A converging lens: the object is 12 cm away, the focal length is 4 cm, and the real inverted image is at 6 cm
LensShapeWhat it does to parallel raysImage from an object outside F
converging (convex)thicker in the middlebrings them together at the principal focusreal, inverted
diverging (concave)thinner in the middlespreads them apart as if from the principal focusvirtual, upright, smaller
Converging and diverging lenses compared

Key ideas

  • Converging lens: parallel rays meet at the principal focus F.
  • Focal length: the distance from the lens centre to F.
  • Object outside F: real, inverted image.
  • Object inside F: virtual, upright, magnified image (the lens works as a magnifying glass).
Worked example 18.4.1
A converging lens has a focal length of 4 cm. A ray parallel to the axis hits the lens. Where does the refracted ray cross the axis? Write the distance in cm from the lens.

Method. A parallel ray is refracted through the principal focus.

  1. Recall. The parallel ray passes through the principal focus, F.
    F
  2. Distance. So it crosses the axis at the focal length, 4 cm from the lens.
    4 cm
  3. Write the answer.
    4 cm

Check. ✓

Worked example 18.4.2
An object is 12 cm from a converging lens of focal length 4 cm. Using the lens equation, find the image distance in cm. Write the number of cm.

Method. Use 1/f = 1/u + 1/v, so 1/v = 1/f - 1/u.

  1. Take the numbers. f = 4 cm and u = 12 cm.
    f = 4, u = 12
  2. Subtract. 1/v = 1/4 - 1/12 = 3/12 - 1/12 = 2/12 = 1/6.
    1/6
  3. Invert. v = 6 cm.
    v = 6
  4. Write the answer.
    6 cm

Check. 1/4 = 1/12 + 1/6. ✓

Worked example 18.4.3
An object is 2 cm from a converging lens of focal length 4 cm. Is the image real or virtual? Write real or virtual.

Method. The object is inside the focal length.

  1. Look. The object (2 cm) is closer than F (4 cm), so it is inside the focal length.
    2 < 4
  2. Decide. The image is virtual, upright and magnified.
    virtual
  3. Write the answer.
    virtual

Check. ✓

Watch out

Watch out: a virtual image cannot be caught on a screen, but a real image can. Do not say a real image is upright when the lens forms an inverted image.

Exam tip

Exam tip. In a ray diagram, use a ruler, draw the principal axis and mark F on both sides at the focal length, and draw the image at the crossing point of two rays.

Exercise 18D  Lenses and ray diagrams

1
FWhich type of lens is thicker in the middle? Write the word: converging or diverging.
2
FWhat is the name of the point where parallel rays meet after passing through a converging lens? Write the name.
3
FWhat is the distance from the lens centre to the principal focus called? Write the name.
4
FIs an image that can be projected on a screen real or virtual? Write the word.
5
FIs an image formed by a magnifying glass real or virtual? Write the word.
6
FWhich type of lens spreads parallel rays out? Write the word: converging or diverging.
7
FA converging lens has a focal length of 5 cm. How far from the lens does a parallel ray cross the axis? Write the number of cm.
8
PSAn object is 20 cm from a converging lens of focal length 5 cm. Find the image distance using 1/v = 1/f - 1/u. Write the number of cm.
9
PSAn object is 10 cm from a converging lens of focal length 5 cm. Find the image distance. Write the number of cm.
10
RIn a ray diagram, a ray through the centre of a converging lens goes straight on. Explain why, in one sentence. Accept any sentence that says the centre of a thin lens acts like a block of glass with parallel faces, so the ray is not bent.
11
RA pupil says “a magnifying glass always forms a real image.” Is the pupil right? Write yes or no.
12
PSA converging lens of focal length 4 cm forms an image of an object placed 3 cm away. Is the image real or virtual? Write the word.
13
RIn the lens practical, a teacher finds the focal length by focusing a distant window on a screen. Why does this work? Write one reason in one sentence. Accept any sentence that says a distant object gives parallel rays, which meet at the focal point.
14
PSA converging lens has a focal length of 10 cm. What is the image distance for an object 10 cm away? Write the word: infinite or a number.
15
PSName the type of lens that forms a virtual, upright and magnified image of a nearby object. Write the word: converging or diverging.

Chapter summary

SkillMethod
Law of reflectionAngle of incidence = angle of reflection, measured from the normal
Plane mirror imageVirtual, upright, same size, as far behind as the object is in front
RefractionTowards the normal when slowing down (entering denser); away when speeding up
[H] Total internal reflectionAbove the critical angle (about 42 degrees for glass to air); optical fibres
Converging lensParallel rays through F; object outside F gives a real inverted image; inside F gives a virtual upright image

Can you…?

  • I can state the law of reflection and describe a plane mirror image
  • I can explain refraction towards and away from the normal
  • [H] I can explain the critical angle and total internal reflection
  • I can draw a ray diagram for a converging lens
  • I can say whether an image is real or virtual

Key terms

normal
the line at right angles to a surface at the point of incidence
refraction
the change of direction of a wave when its speed changes at a boundary
principal focus (F)
the point where rays parallel to the axis meet after a converging lens
focal length
the distance from the lens centre to the principal focus
real image
an image that can be projected on a screen
virtual image
an image that cannot be projected on a screen; the rays only appear to come from it
[H] critical angle
the angle of incidence above which total internal reflection happens

Exercise 18Z  Check-up

1
What is the image in a plane mirror: real or virtual? Write the word.
2
A ray arrives at 15 degrees to the normal of a plane mirror. What is the angle of reflection? Write the number of degrees.
3
When light enters water from air, does it bend towards or away from the normal? Write the word.
4
Name the point where parallel rays meet after a converging lens. Write the name.
5
Is an image formed by a converging lens with the object outside F real or virtual? Write the word.
6
Calculate the image distance for a converging lens of focal length 6 cm with the object 12 cm away. Write the number of cm.
7
[H] Name the angle above which total internal reflection happens. Write the phrase.
8
What is the focal length in cm when the principal focus is 7 cm from the lens centre? Write the number.
9
A ray is parallel to the axis of a converging lens. Where does it go after the lens? Write the word: through F or through the centre.
10
Explain why a plane mirror image cannot be caught on a screen, in one sentence. Accept any sentence that says the light appears to come from behind the mirror, not from a real point.

Total 30 marks. Allow about 30 minutes.

Exercise 18X  Exam-style questions

1
FA ray hits a plane mirror at an angle of incidence of 52 degrees. State the angle of reflection. Write the number of degrees.[1 mark]
2
PSA converging lens has a focal length of 8 cm. An object is 20 cm from the lens. Calculate the image distance. Write the number of cm.[3 marks]
3
RDescribe how to find the focal length of a converging lens using a distant object and a screen. Accept any answer that says focus the image of a distant object on the screen and measure the distance from the lens to the screen.[3 marks]
4
RDescribe the path of light through a rectangular glass block, including what happens at each surface. Accept any answer that says the ray bends towards the normal on entry, travels straight through, and bends away from the normal on leaving.[3 marks]
5
R[H] A ray travels in glass towards the boundary with air at 50 degrees to the normal. The critical angle is 42 degrees. Describe what happens to the ray. Accept any answer that says total internal reflection occurs because the angle is greater than the critical angle.[3 marks]
6
RExplain the difference between a real image and a virtual image, using an example of each. Accept any answer that says a real image can be projected on a screen (e.g. a projector) and a virtual image cannot (e.g. a plane mirror image).[4 marks]
7
RA converging lens with a focal length of 5 cm is used to form an image of an object 4 cm away. Describe the image: real or virtual, upright or inverted, and enlarged or reduced. Accept any answer that says virtual, upright and magnified.[3 marks]
8
RA student draws a ray diagram for a converging lens. Name the three principal rays used to locate the image. Accept any answer that names: the ray parallel to the axis, the ray through the centre, and the ray through the principal focus.[3 marks]
9
PSAn object is 15 cm from a converging lens of focal length 6 cm. Calculate the image distance, and say whether the image is real or virtual. Write two values: the image distance in cm, then real or virtual, separated by a comma.[4 marks]
10
PSA converging lens has a focal length of 10 cm. An object is 30 cm from the lens. Calculate the image distance. Write the number of cm.[3 marks]
← Chapter 17: Waves: transverse, longitudinal and wave speedChapter 19: The electromagnetic spectrum →

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