Measure and calculate plane-mirror constructions
Use scaled geometry to locate images and compare separations after objects or mirrors move.
Section P3.2.1 · Reflection of light
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
- Construct plane-mirror image points.
- Keep object, mirror and image positions distinct.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What should be held explicit when calculating mirror-image movement?
What you will learn
- Use constructions, measurements and calculations for plane mirrors.
- Account for image movement relative to a stated fixed reference.
Make a scaled construction
Choose a diagram scale and mark the reflecting surface and object accurately. Drop a perpendicular from the object point to the mirror, measure that distance and mark an equal distance on the other side. Check with two reflected-ray constructions using local normals and i = r. Image height and perpendicular distances use the same chosen length scale.
For a scale 1 cm : 0.20 m, a real object distance of 0.60 m becomes 3.0 cm on paper and the virtual image is 3.0 cm behind the drawn mirror. A protractor measures angles on the construction directly; an angle is not multiplied by the length scale. Keep rulers aligned perpendicular to the surface for distances.
Keep a fixed coordinate reference for movement
Along a perpendicular x axis a plane mirror at coordinate M images a stationary point O at I = 2M − O. This expresses equal distance on opposite sides, rather than adding a new optical law. If the object moves 0.10 m toward a fixed mirror, the image moves 0.10 m toward it on the other side and their separation falls by 0.20 m.
If instead the mirror moves 0.10 m toward a fixed object, its distance from the object falls by 0.10 m, but the image's position relative to the room changes by 0.20 m toward that object. Do not confuse image movement relative to the mirror with movement relative to the room. State what stays fixed before subtracting positions.
Sources for this lesson
Pause and explain
A mirror moves 6 cm toward a fixed object. How far does the image move relative to the room?
Worked example
A stationary object is at x = 0 and a mirror moves from x = 1.0 m to x = 0.90 m. Find the two image coordinates and image movement.
Show the worked solution
- Initially I = 2(1.0) − 0 = 2.0 m.
- Finally I = 2(0.90) − 0 = 1.80 m.
- The image moves 0.20 m toward the fixed object.
Answer Image 2.0 m → 1.80 m; movement 0.20 m toward the object.
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.
At scale 1 cm : 0.25 m, draw an object 0.75 m from a mirror and locate its image.
Give me a hint
Divide the real distance by the metres represented by one diagram centimetre.
Compare my reasoning
- Object diagram distance = 0.75/0.25 = 3 cm.
- Draw a perpendicular to the surface.
- Mark the image 3 cm behind it.
Object and image are each 3 cm from the drawn mirror.
Look for these in your work
- Use the stated scale.
- Measure perpendicular distances.
An object moves from 40 to 25 cm in front of a fixed mirror. Find the initial and final object–image separations.
Give me a hint
Each separation contains two equal distances.
Compare my reasoning
- Initial separation = 2 × 40 = 80 cm.
- Final separation = 2 × 25 = 50 cm.
- The separation decreases by 30 cm.
80 cm → 50 cm, decreasing by 30 cm.
Look for these in your work
- Use a fixed mirror reference.
- Distinguish distance from separation.
A fixed object has O = 0.20 m. A mirror moves from M = 1.0 to 1.1 m. Find image movement in the room.
Give me a hint
Use equal-distance coordinates for each mirror position.
Compare my reasoning
- Initial I = 2(1.0) − 0.20 = 1.80 m.
- Final I = 2(1.1) − 0.20 = 2.00 m.
- The image moves +0.20 m away from the object.
1.80 m → 2.00 m; +0.20 m away from the object.
Look for these in your work
- Retain the fixed object coordinate.
- State direction and reference.
Common mistakes
- State which object or mirror is fixed.
- Distinguish room and mirror references.
- A length scale does not rescale angles.
What can you explain now?
A fixed mirror images an object moving 5 cm toward it. How far does the image move toward the mirror?
Compare with the explanation
5 cm.
Equal object/image distances each fall by the same 5 cm.
After trying it yourself, choose your next review. This is your self-assessment.
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Make it stick
Construct a scaled mirror image and compare object movement with mirror movement using a fixed reference.
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.