Apply the law of reflection at a plane mirror
Construct the outgoing ray and distinguish the reflection angle from the angle between rays.
Mapped to the named 0654 section using teaching from the corresponding single-science course. A 0654-specific review of every Core and Supplement objective is still in progress. Written practice is self-checked; it does not demonstrate supervised laboratory competence or award an official Cambridge grade.
Before you begin
- Measure ray angles from a normal.
- Recognise a plane surface.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Which reference is shared by i and r?
What you will learn
- Recall and use i = r.
- Predict a reflected direction from the local normal.
Use one normal for the two directions
For reflection at a plane mirror, the angle of incidence equals the angle of reflection: i = r. In a plane construction the reflected ray is on the opposite side of the normal from the incident ray. Draw the normal first, measure i and reproduce that angle on the other side with an arrow leaving the surface.
The equation relates angles to the normal, rather than two arbitrary labels on a drawing. An incidence angle of 35° gives a reflection angle of 35°; each ray makes 55° with the surface. At normal incidence the ray returns along its approach line, with its propagation direction reversed.
State which angle the question requests
The small angle between the drawn incident and reflected arms on the light-facing side is i + r = 2i. For i = 35° that angle is 70°. It is not the reflection angle itself. The change between the travelling incident direction and travelling reflected direction is a different construction, so label arrows and avoid an unqualified 'angle between rays'.
A rough surface still obeys the local reflection law at each illuminated patch, but its normals vary. A wide beam can therefore scatter into several outgoing directions rather than remain a single parallel reflected beam. Equal local angles do not imply that every rough-surface ray leaves in the same direction.
Sources for this lesson
Pause and explain
A ray has i = 48°. What is r?
Worked example
A ray has i = 35° at a plane mirror. Find r and the smaller angle between the two drawn ray arms.
Show the worked solution
- Use i = r to obtain r = 35°.
- Both arms are on opposite sides of the normal.
- Their smaller included angle is 35° + 35° = 70°.
Answer r = 35°; included ray-arm angle 70°.
Try a topic test
Choose Easy, Normal or Difficult. Save your answers and open worked review after finishing.
Test this topic →From guided practice to a new situation
Write your answer and reasoning first. Use a hint only if you are stuck. The model solution is for self-checking; your written work is not automatically marked.
An incoming ray makes 18° with the mirror surface. Find i and r.
Give me a hint
Convert to a normal angle before using the reflection law.
Compare my reasoning
- i = 90° − 18° = 72°.
- Reflection obeys i = r.
- r = 72° to the normal.
i = r = 72°.
Look for these in your work
- Convert the reference.
- Use equal normal angles.
For i = 26°, find r and the angle of the reflected ray to the surface.
Give me a hint
Use the law, then the perpendicular complement.
Compare my reasoning
- r = i = 26°.
- The normal is perpendicular to the surface.
- The outgoing surface angle is 90° − 26° = 64°.
r = 26°; surface angle 64°.
Look for these in your work
- Label both requested angles.
- Avoid doubling i for r.
A rough reflecting surface sends a beam into many directions. Does that observation refute i = r?
Give me a hint
Compare local normals rather than assuming one plane normal everywhere.
Compare my reasoning
- Different surface patches face different directions.
- Each patch has its own normal.
- Local equal-angle reflection can produce several outgoing directions.
No; varying local normals explain the scattered directions.
Look for these in your work
- Apply the local law.
- Distinguish roughness from a failed law.
Common mistakes
- r is measured from the normal.
- Do not replace r with 2i.
- Roughness changes local normals, not the local law.
What can you explain now?
Does normal incidence make the light continue through an opaque mirror?
Compare with the explanation
No.
The reflected ray returns along the same line in the opposite travelling direction.
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Make it stick
Construct an outgoing reflected ray and distinguish normal, surface and included-arm angles.
If you needed the solution, close it and solve the problem again from a blank page. A correct answer is stronger when you can explain the reason for each step.