SCIENCE · INVESTIGATE AND EXPLAIN

Explain focusing changes without a clinical-eye claim

A fixed screen places a stronger constraint than merely asking whether a lens forms some image. For a given object distance and chosen image-plane distance, the required focal length follows 1/f=1/o+1/i. Moving the object while keeping the screen fixed generally requires changing focal length or repositioning optics. The lesson studies that geometric condition, not an individual eye or a medical prescription.

Learning outcome: Compare objects at 20, 40 and 100 cm with the screen fixed at 20 mm. Retain required f, unchanged-lens image coordinate and geometric blur. Then move only the screen and explain which interpretation changes.

Starting recap

Define normal angles and signed object/image distances. Distinguish actual ray intersections from backward extensions, and keep the focal/critical boundaries explicit rather than forcing a finite answer.

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Try

For o=40 cm and screen at 20 mm=2.0 cm, the needed focal length is 1/(1/40+1/2)=1.90476 cm=19.0476 mm. The unchanged 20 mm lens forms its image at 21.0526 mm, beyond the screen. With the stipulated 1 mm semi-aperture, geometric defocus radius is 0.050 mm.

Open the experiment

Predict

As the object moves nearer while the image plane stays fixed, must the needed converging focal length increase or decrease?

Your prediction and reason

Experiment

Compare objects at 20, 40 and 100 cm with the screen fixed at 20 mm. Retain required f, unchanged-lens image coordinate and geometric blur. Then move only the screen and explain which interpretation changes.

Test a fixed image plane without inventing a clinical prescription

Worked teaching model · synthetic values · Ideal thin lens initially f=20 mm; aperture semi-height 1 mm. Real object, fixed screen selected. Compute the focal length needed for that image plane and geometric defocus radius for unchanged lens. No eye anatomy, prescription, diffraction or measured visual acuity is modeled; this is a virtual focusing system.

Object distance: 40 cm Screen distance behind lens: 20 mm

Reset keeps your prediction, captures and practice history.

Axes rescale with settings; compare numerical values, not screen angles or apparent lengths. Solid/points show the selected model relationship or observations; the dashed comparison is explained below.

Calculated evidence ledger — synthetic teaching model
Quantity	Value	Unit
Required focal length for selected screen	19.048	mm
Unchanged lens image distance	21.053	mm
Screen distance	20	mm
Image minus screen offset	1.0526	mm
Geometric defocus radius	0.05	mm

Accessible plot coordinates

Primary plotted points
object distance (cm)	focal length needed for screen (mm)
20	18.182
25	18.519
30	18.75
35	18.919
40	19.048
45	19.149
50	19.231
55	19.298
60	19.355
65	19.403
70	19.444
75	19.481
80	19.512
85	19.54
90	19.565
95	19.588
100	19.608

Moving the object changes the focal length needed to keep an image on the same screen.

The unchanged lens has f=20 mm. Defocus radius uses a 1 mm aperture semi-height and similar triangles, not diffraction or a clinical acuity model. Zero geometric defocus is not proof of a perfect real image. No sunlight focusing, lasers, eye testing or medical prescription is requested.

Moving the object changes the focal length needed to keep an image on the same screen.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

Establish the model and evidence

The model starts with a thin lens of focal length 20 mm and a selected screen behind it. It calculates where the unchanged lens would form its image and compares that coordinate with the screen. It separately reports the focal length that would put the image on the selected screen. These are different hypotheses, not simultaneous claims that one lens has both focal lengths.

For a small aperture, similar triangles give a geometric defocus radius on a displaced screen. The model uses an aperture semi-height of 1 mm and radius proportional to |1−screen/image distance|. This is a ray-only estimate, not a diffraction blur, visual-acuity metric or image-quality guarantee. Reducing an aperture would reduce this geometric blur but can increase wave diffraction, which this lesson does not calculate.

An optical system may actively change lens curvature or position to keep an image plane fixed. That qualitative principle can help explain focusing systems, but real eyes include multiple surfaces and biological constraints. The numbers here are hypothetical and must not be used to infer a prescription, disease or safe viewing condition. No eye testing, sunlight concentration or intense-light activity is requested.

Worked evidence

Predict and investigate

As the object moves nearer while the image plane stays fixed, must the needed converging focal length increase or decrease?

Transfer to changed conditions

A hypothetical screen is 25 mm behind a thin lens and the object is 50 cm away. Find the focal length needed to focus on that screen.

Compare the worked transfer

Convert image distance to 2.5 cm. f=1/(1/50+1/2.5)=2.38095 cm=23.8095 mm. This is a hypothetical geometrical focusing value, not a clinical prescription.

Explain the boundary

Why would zero geometric defocus not prove a perfect real optical image or normal vision?

Sources and authorship

Physical relationship reference. Current AP Physics 2 framework, checked 30 October 2026. Original text, rays and computed/synthetic records, not completed optical measurements. All investigations are virtual: no lasers, intense-light viewing, sunlight focusing, flames or eye tests are requested. Any real practical work needs qualified supervision and independent safety review.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Why would zero geometric defocus not prove a perfect real optical image or normal vision?

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Challenge a lens fit with distance-reference errors Next: Read a wave snapshot without mistaking it for particle travel

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