Reflection of light
Key idea: The angle of reflection equals the angle of incidence, both measured from the normal. Draw the reflected ray leaving the mirror on the other side of the normal.
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Guided lessons · coming soon
Guided lesson
Guided steps
- Measure reflection angles from the normal.
- Convert the surface angle to incidence.
- Find the incidence angle for each ray.
- Follow the reflected ray using equal angles.
- Draw the reflected ray on paper.
- Explain how measuring from the wrong line changes an angle.
- Compare the angle between rays with the change in direction.
- Find reflection and ray-segment angles from the surface angle.
- Apply reflection at each periscope mirror.
- Sketch the corner-mirror path, then check its angles and direction.
- Check whether the tilted mirror sends light straight down.
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ContinueWhen light meets a mirror, it bounces off in a direction you can predict exactly. One rule, the law of reflection, fixes that direction, so with a ruler and a protractor you can draw where any reflected ray goes, from a bathroom mirror to the two mirrors inside a periscope. A ray is a line with an arrow that shows the direction light travels.
Describe reflection from the normal
The point where a ray meets the mirror is the point of incidence. Every angle in reflection is measured from one construction line drawn there.
| Term | Meaning |
|---|---|
| Incident ray | The ray arriving at the mirror. |
| Reflected ray | The ray leaving the mirror. |
| Normal | A line at 90° to the mirror at the point of incidence. Draw it dashed: it is a construction line, not a ray. |
| 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. |
A question often gives the angle between the ray and the mirror surface instead. The normal is at 90° to the surface, so the two angles add up to 90°:
Worked example 1
Finding i from the angle to the mirror
Problem
A ray strikes a plane mirror at 32° to its surface. Find the angle of incidence.
Show full solution
Check which angle you are given
Method
The 32° is measured from the mirror surface.Reason
The angle of incidence is defined from the normal, not from the surface.
Working
Answer
So 32° is not i.
Use the right angle
Method
The normal and the surface are at 90° to each other.Reason
The angle to the surface and the angle to the normal share that 90°.
Working
Answer
i = 90° - 32° = 58°
State the angle of incidence
Working
Answer
The angle of incidence is 58° from the normal.
Quick check
A ray that just skims the mirror has a small angle to the surface but a large angle of incidence, close to 90°.
Check your understanding 1 Read the given reference line
Show answer
For the first ray, incidence is 90° − 25° = 65°, measured from the normal. A ray travelling along the normal has 0° incidence and is reflected back along the same line; its angle to the mirror surface is 90°. These are different reference lines.
The law of reflection
For reflection at a mirror:
The incident ray, the reflected ray and the normal also lie in the same flat plane, so on paper you draw all three on the page. The reflected ray is on the other side of the normal from the incident ray, and on the same side of the mirror.
Construct a reflected ray
Use a sharp pencil, a ruler and a protractor.
- Draw the mirror line and the incident ray, with an arrow. Mark the point of incidence P.
- Draw the normal at P, at 90° to the mirror, as a dashed line.
- Measure i between the incident ray and the normal.
- Measure the same angle on the other side of the normal. Draw the reflected ray from P and add an arrow pointing away from the mirror.
Check your understanding 2 Construct a reflected ray
On paper, draw a horizontal mirror and an incident ray striking it at 30° to its surface. Construct the reflected ray with a ruler and protractor, then compare your construction. Check the point of incidence, normal, angles and arrows against the answer.
Show answer
Draw the mirror line and the incident ray with an arrow, and mark P. Draw the normal at P at 90° to the mirror. The angle of incidence is 90° − 30° = 60°. Measure 60° from the normal on the other side and draw the reflected ray from P, with an arrow pointing away from the mirror.
Measure i and r with a ray box
You can check the law with a ray box, which sends out a narrow beam of light.
- Draw a line on paper and stand the reflecting surface of a plane mirror on it.
- Draw a normal to the line and a line at a chosen angle i to it.
- Shine the ray from the ray box along the drawn line, so that it reaches the mirror where the normal meets it.
- Mark the reflected ray with two small crosses, far apart.
- Remove the mirror, join the crosses back to the point of incidence and measure r from the normal.
- Repeat for several angles of incidence.
| i / ° | r / ° |
|---|---|
| 20 | 21 |
| 35 | 35 |
| 50 | 49 |
| 65 | 65 |
Each r is within 1° of its i. Such small differences are consistent with uncertainty in locating the beam centre and reading the protractor. If the estimated uncertainty in each angle is about 1°, these readings support i = r within that uncertainty; the readings alone do not identify the cause of each difference. The light investigations lesson shows another method, using pins.
Check your understanding 3 Readings that do not match
A student records i = 25° and r = 65° for a ray reflected by a plane mirror. Suggest an angle-measuring mistake that could explain these readings.
Show answer
One angle was probably measured from the mirror surface instead of the normal, because 25° + 65° = 90°. If i was measured correctly, both angles are 25°; if r was measured correctly, both are 65°. The readings alone do not show which one is wrong.
Calculate angles at one mirror
At the mirror, the angle between the two ray segments on the reflecting side is i + r = 2i. The change in the direction of travel is a different angle: 180° − 2i. For example, a ray along the normal has i = 0° and retraces its path, changing its travel direction by 180°.
Worked example 2
From the angle between the rays to i
Problem
The angle between an incident ray and its reflected ray is 110°. Find the angle of incidence and the angle the reflected ray makes with the mirror.
Show full solution
Split the angle at the normal
Method
The normal lies between the two rays.Reason
The 110° is made up of i on one side of the normal and r on the other, and i = r.
Working
Answer
i + r = 2i = 110°, so i = 55° and r = 55°.
Convert to the angle with the mirror
Method
Use the right angle between the normal and the mirror.
Reason
The reflected ray’s angle to the mirror and its angle to the normal add to 90°.
Working
Answer
90° - 55° = 35° to the mirror.
State both angles
Working
Answer
The angle of incidence is 55°. The reflected ray makes 35° with the mirror.
Quick check
Check: 2 × 55° = 110°, the angle given, and 55° + 35° = 90°. Halving the angle between the rays gives the angle to the normal, not to the mirror.
Check your understanding 4 From the surface angle
A ray strikes a mirror at 20° to its surface. Find the angle of reflection and the angle between the incident and reflected ray segments.
Show the steps Optional working
Show answer
i = 90° − 20° = 70°, so r = 70°. The angle between the rays is i + r = 140°.
Two mirrors: the periscope
A periscope lets you see over a wall. It has two plane mirrors, parallel to each other, each at 45° to the tube. Apply the law of reflection at each mirror in turn.
Worked example 3
Tracing a ray through a periscope
Problem
A horizontal ray enters the top of the periscope in the figure. Find i and r at each mirror and the direction of the ray when it leaves.
Show full solution
Top mirror
Method
The horizontal ray meets the top mirror at 45° to its surface.
Reason
i is measured from the normal, which is at 90° to the mirror.
Working
Answer
i = 90° - 45° = 45°, so r = 45°. The angle between the rays is 2 × 45° = 90°: the ray now travels straight down the tube.
Bottom mirror
Method
The vertical ray meets the bottom mirror, which is parallel to the top one.
Reason
The bottom mirror is also at 45° to the vertical ray.Working
Answer
i = 45° and r = 45°, so the ray turns through 90° again.
State the direction
Working
Answer
The ray leaves horizontally, travelling the same way it entered. The emergent ray is parallel to the incident ray, so an observer looking horizontally into the bottom mirror sees what is in front of the top opening.
Quick check
Construct it yourself: draw each normal at 90° to its mirror and measure 45° on each side. Your emergent ray should be parallel to the incident ray.
Guided practice 4
Two mirrors at right angles
Problem
Two plane mirrors meet at 90°, like the corner of a box: mirror A is horizontal and mirror B is vertical. A ray strikes mirror A with an angle of incidence of 30°, reflects, and then strikes mirror B. Sketch the path. Find the angle of incidence at B and describe the final ray.
Try this before viewing the solution
Hints
Hint 1
find the normals
A’s normal is vertical. B’s normal is horizontal, which makes it parallel to mirror A.
Hint 2
angle at mirror B
The angle the ray makes with mirror A is the same as the angle it makes with B’s normal, because those two lines are parallel.
Show solution step by step
Reflect at A
Method
Apply i = r at mirror A.Reason
The reflected ray makes 30° with A’s vertical normal.Working
Answer
It makes 90° - 30° = 60° with mirror A.
Find i at B
Method
Measure from B’s normal, which is horizontal.Reason
B’s normal is parallel to mirror A, so the ray meets it at the same 60°.
Working
Answer
iB = 60°, so rB = 60°.
Describe the final ray
Working
Answer
The ray leaves B travelling back parallel to its original path. Notice that 30° + 60° = 90°: for mirrors at right angles, the two angles of incidence always add to 90°.
Quick check
Check with a construction: draw the corner, the first ray and each normal, and measure. If the final ray is not parallel to the first, recheck both normals, the angles measured from them and the ray arrows.
Check your understanding 5 A tilted mirror
A periscope’s top mirror is at 50° to the horizontal, tilted to reflect a horizontal incoming ray downwards. Find the angle of incidence and the angle between the two ray segments. Does the reflected ray travel straight down the vertical tube?
Show the steps Optional working
Show answer
The ray is at 50° to the mirror, so i = 90° − 50° = 40° and r = 40°. The angle between the rays is 2 × 40° = 80°, not 90°, so the reflected ray is 10° away from the vertical and does not travel straight down the tube.
Common mistakes
- Measuring i or r from the mirror surface. Both are measured from the normal; if you are given the angle to the surface, subtract it from 90°.
- Drawing the normal away from the point of incidence, or not at 90° to the mirror.
- Drawing the reflected ray behind the mirror, or on the same side of the normal as the incident ray.
- Taking the angle between the two rays as i. That angle is i + r = 2i, so halve it.
- Leaving out the arrows that show which way the light travels.
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Syllabus and review details
- SEC G3 Combined Science Physics component 2027 · 2027
Physics section, PDF pages 8–24
Last reviewed: