Locate principal axis focus and focal length
Define lens references before measuring distances or constructing image rays.
Cross-referenced to the 2028–2029 0653 section using original teaching from the related single-science courses. A 0653-specific objective-by-objective and Core/Supplement review is in progress. Written practice is self-checked and does not demonstrate supervised laboratory competence or award an official Cambridge grade.
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.
Sources for this lesson
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.
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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.