Explain converging-lens correction of long-sightedness
Compare insufficient near-object convergence with the extra convergence needed at the retina.
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
- Know that near-object rays diverge before the eye.
- Describe converging lens action.
Work on paper. Try each question before revealing help, and explain why your method works.
Quick readiness check
Before reaching the eye, how do rays from a nearby point object travel?
What you will learn
- Describe long-sightedness in a near-object eye model.
- Explain converging-lens correction toward the retina.
Use the near-object focusing case
A nearby object sends diverging light toward the eye. In the simple long-sighted-eye model, the available eye convergence is insufficient for that near object, so the rays would focus behind the retina. At the retina they are still converging and have not yet met, giving a blurred near-object image in the model.
The focus behind the retina is an extrapolated continuation of actual forward ray directions, not the virtual backward-extension image used for a magnifier. Keep the near-object condition explicit and distinguish the optical focusing error from claims about all possible eye conditions or every person's distance vision.
Add convergence before the eye
A converging external lens supplies additional convergence to the near-object bundle before it reaches the eye. With a suitable correcting lens in the illustrated model, the eye brings the rays to a real focus on the retina instead of beyond it. The retina stays in the same position while the input directions change.
Compare the two correction types: a short-sighted distant-object model needs diverging correction to move an early focus back; a long-sighted near-object model needs converging correction to bring a late focus forward. A qualitative diagram explains lens type and mechanism but does not provide personal measurements or an individual prescription.
Sources for this lesson
Pause and explain
A near object's focus would lie behind the retina. Which correcting action is needed?
Worked example
A supplied near-object eye model would focus beyond the retina. Explain the correcting lens type.
Show the worked solution
- The input is a diverging near-object bundle.
- The available eye convergence does not bring it together soon enough.
- A converging correcting lens adds convergence so the eye can focus at the retina.
Answer A converging lens brings the intended near-object focus forward to the retina.
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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.
Describe the near-object focus error in the long-sighted model.
Give me a hint
Compare where the rays would meet with the receiving surface.
Compare my reasoning
- Near-object light arrives as a diverging bundle.
- The eye's available action would focus it behind the retina.
- At the retina the rays are still converging, giving blur.
The near-object focus lies behind the retina in the uncorrected model.
Look for these in your work
- Specify the near-object case.
- Locate the focus correctly.
Explain how a converging correcting lens addresses it.
Give me a hint
Add external convergence before the eye acts.
Compare my reasoning
- The lens changes the incoming near-object ray directions.
- It adds convergence to the bundle.
- The eye can then focus the rays earlier, on the retina in the corrected model.
Additional external convergence brings the focus forward onto the retina.
Look for these in your work
- State lens type and action.
- Keep the retina fixed.
Contrast the correcting lenses for the supplied short-sighted distant and long-sighted near models.
Give me a hint
Match each lens action to the focus being too early or too late.
Compare my reasoning
- Short-sighted distant focus is before the retina.
- A diverging lens moves that focus back.
- Long-sighted near focus is behind the retina; a converging lens brings it forward.
Short-sighted: diverging; long-sighted: converging, for the stated models.
Look for these in your work
- Name both focus errors.
- Explain the opposite correction actions.
Common mistakes
- Long-sighted near-object focus is behind the retina.
- Use converging correction for this model.
- A late forward focus is not a backward-extension virtual image.
What can you explain now?
Does the correcting lens need to shift the retinal receiving surface?
Compare with the explanation
No.
It alters incident ray directions to focus at the existing retinal plane.
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Make it stick
Explain the long-sighted near-object focus and contrast its correction with the short-sighted model.
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