📐 A ray at an angle
The incident ray and the reflected ray make equal angles with the normal, one on each side of it.
Light and Sound » Reflection of Light
What you'll learn this session
Study time: 30 minutes
Edexcel spec: 3.14, 3.15, 3.16
- That light waves are transverse waves that can be reflected and refracted
- The law of reflection and how to use it to work out angles
- How to draw a ray diagram for reflection, step by step
- What to do when a question gives the angle to the mirror
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Unlock This CourseLight is a transverse wave
Light is a wave. Remember, light is part of the electromagnetic spectrum, and all electromagnetic waves are transverse. So light waves are transverse waves. Learn that sentence, because it is an easy mark.
Like other waves, light can be:
- reflected, when it bounces off a surface, such as a mirror
- refracted, when it changes direction as it passes from one material into another, such as from air into glass
This lesson is about reflection. Refraction comes next, in Refraction of Light.
Light travels in straight lines. To show where it goes, we draw a ray: a straight line with an arrow on it. A drawing made of rays is called a ray diagram.
Key terms:
- Ray: a straight line with an arrow that shows the path and direction of light.
- Ray diagram: a drawing that uses rays to show what happens to light.
- Plane mirror: a flat mirror.
- Incident ray: the ray of light travelling towards the mirror.
- Reflected ray: the ray of light travelling away from the mirror after it has been reflected.
- Normal: a line drawn at right angles (90°) to the mirror at the point where the incident ray hits it.
- Angle of incidence (i): the angle between the incident ray and the normal.
- Angle of reflection (r): the angle between the reflected ray and the normal.
The law of reflection
When light reflects from a plane mirror, it always obeys one simple rule, called the law of reflection:
The law of reflection
angle of incidence = angle of reflection
In symbols: i = r
Both angles are measured from the normal, not from the mirror.
So if a ray hits a mirror with an angle of incidence of 30°, it leaves with an angle of reflection of 30°. If the angle of incidence is 70°, the angle of reflection is 70°. The ray leaves on the other side of the normal, like a ball bouncing off the cushion of a snooker table.
The normal is not a ray of light. It is a guide line that we add to the diagram so that we have something to measure the angles from. That is why it is drawn as a dashed line.
🔦 A ray along the normal
If the ray hits the mirror at right angles, the angle of incidence is 0°. The angle of reflection is also 0°, so the light goes straight back the way it came.
How to draw a ray diagram for reflection
You may be asked to draw or complete a ray diagram in the exam. Use a sharp pencil, a ruler and a protractor, and follow these steps.
- Draw the mirror. Rule a straight line. Add short slanted lines (hatching) along the back of it to show which side is not shiny.
- Draw the incident ray. Rule a straight line that meets the front of the mirror. Put an arrow on it, pointing towards the mirror.
- Draw the normal. At the point where the incident ray touches the mirror, draw a dashed line at 90° to the mirror. Use a protractor or a set square to get the right angle.
- Measure the angle of incidence. Put the centre of the protractor on the point where the ray meets the mirror, with its zero line along the normal. Read the angle between the incident ray and the normal.
- Mark the angle of reflection. On the other side of the normal, make a small mark at the same angle.
- Draw the reflected ray. Rule a straight line from the point on the mirror through your mark. Put an arrow on it, pointing away from the mirror.
- Label the angles. Write i between the incident ray and the normal, and r between the reflected ray and the normal.
The finished diagram looks like a letter V standing on the mirror, with the dashed normal straight up the middle. When a ray hits a mirror at an angle, the two sides of the V lean by the same amount.
| Part of the diagram | How to draw it |
|---|---|
| Mirror | solid straight line with hatching on the back |
| Normal | dashed line at 90° to the mirror, no arrow |
| Incident ray | solid ruled line with an arrow towards the mirror |
| Reflected ray | solid ruled line with an arrow away from the mirror |
| Angles i and r | between each ray and the normal |
Working out angles
Many questions give you one angle and ask for another. The normal is at 90° to the mirror, so the angle between a ray and the mirror and the angle between the same ray and the normal always add up to 90°.
Worked example 1
Question: A ray of light hits a plane mirror with an angle of incidence of 35°. State the angle of reflection.
Answer: angle of reflection = angle of incidence = 35°
Worked example 2: the angle to the mirror is given
Question: A ray of light hits a plane mirror. The angle between the ray and the mirror is 25°. Calculate the angle of reflection.
Answer: First find the angle of incidence, which is measured from the normal.
angle of incidence = 90° − 25° = 65°
angle of reflection = angle of incidence = 65°
The reflected ray also makes an angle of 25° with the mirror, because 90° − 65° = 25°.
Worked example 3: the angle between the two rays is given
Question: The angle between an incident ray and its reflected ray is 80°. Calculate the angle of incidence.
Answer: The normal splits this angle into two equal parts, because i = r.
angle of incidence = 80° ÷ 2 = 40°
Worked example 4: a periscope mirror
Question: A simple periscope uses plane mirrors tilted so that light hits each one with an angle of incidence of 45°. Calculate the angle between the incident ray and the reflected ray at one mirror.
Answer: angle of reflection = angle of incidence = 45°
angle between the incident ray and the reflected ray = 45° + 45° = 90°
So the reflected ray leaves each mirror at a right angle to the incident ray.
Common mistakes
- Measuring the angles from the mirror. Both angles are measured from the normal.
- Using the angle to the mirror as the angle of incidence. If you are given the angle to the mirror, subtract it from 90° first.
- Leaving the arrows off the rays. A line with no arrow does not show which way the light is travelling.
- Drawing the normal as a solid line or putting an arrow on it. The normal is a dashed guide line, not a ray.
- Drawing rays freehand. Always use a ruler, because light travels in straight lines.
- Drawing the normal in the wrong place. It must start at the point where the incident ray meets the mirror.
- Writing that light is a longitudinal wave. Light waves are transverse.
Exam-style question
A student shines a ray of light at a plane mirror. The angle between the incident ray and the mirror is 28°.
(a) State whether light waves are transverse or longitudinal. [1 mark]
(b) State what is meant by the normal. [1 mark]
(c) Calculate the angle of incidence. [2 marks]
(d) State the angle of reflection and give a reason for your answer. [2 marks]
(e) Describe how the student should add the reflected ray to a ray diagram that already shows the mirror and the incident ray. [3 marks]
Model answer
(a) Transverse (1).
(b) A line at right angles (90°) to the mirror at the point where the ray hits it (1).
(c) Angle of incidence = 90° − 28° (1) = 62° (1).
(d) 62° (1), because the angle of incidence equals the angle of reflection (1).
(e) Draw a dashed normal at 90° to the mirror where the incident ray meets it (1). Use a protractor to mark 62° from the normal on the other side (1). Rule a straight line from the mirror through the mark, with an arrow pointing away from the mirror (1).
Exam tip
Read the first line of an angle question twice. Here the 28° is the angle to the mirror, so writing 28° in parts (c) and (d) would lose the marks. Sketch the normal on the diagram straight away and you will see which angle you have been given.