Explain diverging-lens correction of short-sightedness
Compare a distant object's premature focus with the less-converging bundle needed at the retina.
Extended only (Supplement); 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 converging and diverging beam actions.
- Know the retina receives an eye's real image.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Where is the uncorrected distant focus for short-sightedness in this model?
What you will learn
- Describe short-sightedness in the school eye model.
- Explain how a diverging correcting lens moves focus to the retina.
Compare the focal position with the retina
In the simple short-sighted-eye model, rays from a distant object are nearly parallel before entering the eye. The eye's optical system brings them to a focus in front of the retina rather than on it. At the retinal plane the rays have crossed and spread again, giving a blurred distant-object image in that model.
The retina is a physical receiving surface and the focused retinal image is real. Short-sightedness is not described by a virtual image forming directly on the retina or by every incoming ray failing to enter the eye. The model compares focus and retinal positions for the distant-object condition.
Reduce the incoming convergence
A diverging correcting lens spreads the incoming nearly parallel bundle before the eye. The eye then receives a suitable diverging input and focuses it farther back, on the retina in the illustrated corrected model. The external lens changes the incident directions; it does not physically move the retina.
Use qualitative ray directions rather than claiming one unspecified lens strength corrects every person. The educational diagram supplies a simplified optical comparison, not an individual prescription or a diagnosis. Lens powers, distances and the actual eye would require further data to calculate a specific correction.
Pause and explain
Which lens corrects the stated short-sighted distant-object model?
Worked example
A distant object's focus lies in front of the retina in a supplied eye model. Which correcting lens is appropriate and why?
Show the worked solution
- The eye focuses the parallel bundle too early.
- A diverging external lens spreads the incoming rays.
- The corrected input can be focused farther back onto the retina.
Answer A diverging lens reduces the incoming convergence and moves the focus to the retina in this model.
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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.
Explain the distant-object focus problem in short-sightedness.
Give me a hint
Compare the actual crossing with the retinal plane.
Compare my reasoning
- Distant rays arrive nearly parallel.
- The uncorrected eye focuses them before the retina.
- The retinal plane receives a spread bundle rather than the sharp crossing.
Distant real focus lies in front of the retina, giving blur there.
Look for these in your work
- Specify distant input.
- Locate the focus relative to the retina.
Explain how a diverging lens changes this focus problem.
Give me a hint
Follow the input bundle before considering the eye's convergence.
Compare my reasoning
- The correcting lens makes incoming rays diverge.
- The eye receives a less-converging input condition.
- Its real focus is moved farther back to the retinal plane in the corrected model.
Diverging input shifts the eye's focus back onto the retina.
Look for these in your work
- Describe the external lens action.
- Retain the fixed retinal position.
Can this qualitative comparison determine the exact correcting lens strength for a particular student?
Give me a hint
The sketch does not supply that person's measured optical data.
Compare my reasoning
- The diagram identifies the type of required action.
- It lacks individual distances and focusing measurements.
- It does not establish a numerical prescription.
No; it teaches the correction mechanism, not an individual lens strength.
Look for these in your work
- Separate mechanism from quantity.
- Identify missing measurements.
Common mistakes
- Short-sighted distant focus is in front of the retina.
- Use a diverging correction for this model.
- Do not infer an individual lens strength from the qualitative sketch.
What can you explain now?
Does the correcting lens need to move the retina?
Compare with the explanation
No.
It changes incoming ray directions so the eye's focus reaches the same retinal plane.
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Make it stick
Explain the short-sighted distant focus and why a diverging lens provides the intended correction.
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.