Locate principal axis focus and focal length
Define lens references before measuring distances or constructing image rays.
Core and Extended; Physics 0625, 2026–2028. Follow the selected Light section; ray diagrams use an ideal thin-lens or plane-boundary model. Written work is self-checked.
Before you begin
- Compare parallel-beam actions.
- Use a length scale on a diagram.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
From where is focal length measured in the thin-lens model?
What you will learn
- Define principal axis and principal focus.
- Measure focal length from the optical centre.
Define the three references
The principal axis is the lens's central symmetry line through its optical centre. For a thin converging lens, the principal focus is where rays initially parallel to that axis converge after transmission. For a thin diverging lens it is the apparent origin found by extending the diverging output backward.
Focal length is the distance from the optical centre to the principal focus. It is a length, not an incidence angle or an image's height. The ideal lens has corresponding focal points on either side; choose the relevant one for the incoming direction and the lens action used in the construction.
Read the length rather than another feature
If the optical centre is at a 20 cm ruler position and the appropriate focus at 35 cm, the focal length is 15 cm. Positions are separate ruler coordinates; the requested distance is their difference. Measure along the principal axis, not along a sloping ray from the top of an object.
A distant object gives nearly parallel incident rays, so a converging lens can form a sharp real image near its principal focus. A suitable teacher-supervised distant-object method measures lens-to-screen separation at focus. A finite nearby object need not form its image exactly one focal length away, so an arbitrary focused image distance is not automatically f.
Pause and explain
Centre x = 18 cm, focus x = 30 cm: what is f?
Worked example
On a scaled axis the lens centre is x = 20 cm and the focus is x = 35 cm. Find f.
Show the worked solution
- Identify the centre and the relevant focus.
- Subtract their axis coordinates.
- f = 35 − 20 = 15 cm.
Answer Focal length 15 cm.
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.
Define the principal focus of a converging lens.
Give me a hint
Specify the incident beam before describing the crossing.
Compare my reasoning
- Use rays initially parallel to the principal axis.
- Follow them through the lens.
- Their real crossing on the far side is the principal focus.
Far-side crossing of an initially parallel axial beam.
Look for these in your work
- Specify parallel input.
- Identify actual convergence.
The lens centre is at 42 cm and a marked principal focus is at 27 cm. Find f.
Give me a hint
A distance is the positive separation of the coordinates.
Compare my reasoning
- The focus is on the other side of the centre.
- Separation = 42 − 27.
- f = 15 cm.
15 cm.
Look for these in your work
- Use coordinate difference.
- Give a positive distance.
A nearby object is focused on a screen 30 cm from a lens. Does that measurement alone prove f = 30 cm?
Give me a hint
Consider what incident beam defines the principal focus.
Compare my reasoning
- A nearby object sends a diverging beam.
- The principal focus is defined by parallel axial input.
- The nearby-object image distance alone does not establish f.
No; a nearby-object image distance is not automatically focal length.
Look for these in your work
- State the defining beam.
- Reject an unsupported measurement interpretation.
Common mistakes
- Measure from the optical centre.
- Focal length is not every object or image distance.
- Use the relevant focus for the incoming direction.
What can you explain now?
Does a nearby object's real image have to form at F?
Compare with the explanation
No.
F defines the parallel axial beam's image point; nearby objects generally form elsewhere.
After trying it yourself, choose your next review. This is your self-assessment.
Your review choice appears on Today. Sign in to sync it across devices.
Make it stick
Define principal axis, focus and focal length, then distinguish f from a general image distance.
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.