Compare converging and diverging lenses on parallel beams
Trace parallel rays toward a real focus or away from an apparent focus.
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
- Represent light direction with ray arrows.
- Distinguish real paths and dashed constructions.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
What happens to a parallel axial beam at a converging lens?
What you will learn
- Describe thin converging and diverging lens action.
- Distinguish actual convergence from backward extensions.
A converging lens brings parallel rays together
In the ideal thin-lens model, a beam parallel to the principal axis is brought together by a converging lens at its principal focus on the far side. Rays above and below the axis bend toward it. Light actually crosses at that real focus; an appropriate screen placed there can receive the concentrated beam from a distant source.
A thin converging glass lens in air is usually thicker near the centre than its edges. Its action follows refraction at its surfaces, represented by one change at the lens plane in a thin-lens diagram. The simple diagram is an approximation for suitable rays, rather than a claim that every thick or strongly off-axis real lens makes a perfect point.
A diverging lens spreads parallel rays
A thin diverging lens makes a parallel beam spread out after transmission. The outgoing rays' backward dashed extensions meet at the principal focus on the incident side. That focus is apparent: the outgoing light does not physically meet there. The diverging lens is usually thinner near the centre than its edges for glass in air.
The focus is defined for a beam parallel to the principal axis, not every arbitrary incoming direction. A ray passing through the optical centre is drawn straight in the ideal thin-lens construction. Put arrows on actual paths and reserve dashed lines for backward extensions so a diverging sketch is not mistaken for physical rays travelling backward.
Sources for this lesson
Pause and explain
Where is the principal focus of a diverging lens for an incoming parallel beam?
Worked example
Compare a parallel axial beam after a converging lens and after a diverging lens.
Show the worked solution
- The converging lens brings actual rays to a far-side focus.
- The diverging lens sends actual rays outward.
- Backward extensions of the diverging rays meet at a near-side apparent focus.
Answer Converging: real far-side focus; diverging: apparent incident-side focus.
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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.
Sketch the action of a converging lens on three rays parallel to its axis.
Give me a hint
Keep the central ray straight and direct the others toward one focus.
Compare my reasoning
- Draw the principal axis and lens plane.
- Draw incoming parallel rays with forward arrows.
- Make the transmitted rays meet at the far-side focus.
Actual transmitted rays converge at the far-side focus.
Look for these in your work
- Include travel arrows.
- Use one consistent focus.
Sketch a diverging lens's action on a parallel beam and locate its focus.
Give me a hint
Separate outgoing physical rays from backward constructions.
Compare my reasoning
- Draw transmitted rays spreading apart.
- Extend them backward with dashed lines.
- The extensions meet at an incident-side apparent focus.
Outgoing divergence with a virtual incident-side focus.
Look for these in your work
- Use dashed extensions.
- Place the focus on the correct side.
A diagram shows solid arrows travelling backward from a diverging lens to its focus. Explain the error.
Give me a hint
The focus construction is apparent rather than a second physical beam.
Compare my reasoning
- The real transmitted rays travel forward and diverge.
- Backward lines are extrapolations used to locate an apparent origin.
- Use dashed extensions without representing physical backward travel.
Replace the backward physical rays with dashed construction extensions.
Look for these in your work
- Retain actual ray direction.
- Distinguish the apparent focus.
Common mistakes
- Do not draw virtual extensions as real backward rays.
- Specify a beam parallel to the principal axis.
- The ideal thin-lens picture has a stated model scope.
What can you explain now?
Do outgoing rays of a diverging lens physically meet at its apparent focus?
Compare with the explanation
No.
Only their backward extensions meet there.
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Make it stick
Sketch the two parallel-beam actions and explain real versus apparent principal focus.
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.