SCIENCE · INVESTIGATE AND EXPLAIN

Keep lens power, image distance and orientation distinct

A thin lens bends paraxial rays as though the refraction occurred at one plane. In the same surrounding medium on both sides, a converging lens has positive focal length and a diverging lens negative focal length. A real object before the lens has positive object distance. Positive image distance is after the lens, unlike the mirror convention in which a positive real image lies back in front of the reflecting surface.

Learning outcome: Compare o=6,12,18,36 cm for a converging lens and one matching diverging-lens case. Retain signed image coordinates and magnification separately. Use a third ray to check a first two-ray construction and name a physical assumption that could invalidate the thin-lens result.

Starting recap

Use normal-based angles, signed conjugate distances and explicit optical-path/reflection phases. Separate geometric direction, amplitude and energy; preserve focal and critical boundaries.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

For f=12 cm and o=18 cm, i=36 cm and m=−2. Lens power is1/.12≈8.33333 inverse metres, not1/12 inverse metres. At o=6 cm, i=−12 cm and m=+2. The latter image is virtual and on the incident side; at o=12 cm there is no finite image.

Open the experiment

Predict

A converging lens has f=12 cm. What is its optical power?

Your prediction and reason

Experiment

Compare o=6,12,18,36 cm for a converging lens and one matching diverging-lens case. Retain signed image coordinates and magnification separately. Use a third ray to check a first two-ray construction and name a physical assumption that could invalidate the thin-lens result.

Classify thin-lens conjugates before placing a screen

Worked teaching model · synthetic values · Paraxial thin lens in the same surrounding medium on both sides, f=12b cm, real object height1 cm. Positive i is after the lens; negative i is a virtual image before it. Lens power uses f in metres. Exact focal object gives parallel outgoing rays, not a finite screen image.

Object distance before lens: 18 cm Lens focal sign: -1 diverging, +1 converging: 1 sign

Reset keeps your prediction, captures and practice history.

Paraxial lens object and image locations

Spatial axes use the same pixels per physical unit, preserving geometry. 1: object before optical surface (solid).2: real image (dashed).3: optical surface (dotted).4: optical axis extent (dotted). Joined curves show the supplied model, not additional observations.

Equivalent numerical coordinates for Paraxial lens object and image locations

object before optical surface

axis coordinate (cm)	height (cm)
-18	0
-18	1

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

real image

axis coordinate (cm)	height (cm)
36	0
36	-2

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

optical surface

axis coordinate (cm)	height (cm)
0	-2
0	2

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

optical axis extent

axis coordinate (cm)	height (cm)
-36	0
36	0

At most 82 representative computed coordinates including endpoints; the plotted curve can use a finer grid. A table of a revealed generator is not independent measurement evidence.

Calculated quantities under the declared measurement model
Quantity	Value	Unit
Signed focal length	12	cm
Object distance	18	cm
Object at focal distance	0	flag
Optical power from focal length	8.33333	m⁻¹
Signed image distance	36	cm
Transverse magnification	-2	ratio
Image height	-2	cm
Real image branch	1	flag
Reciprocal equation residual	0	cm⁻¹

The model forms a real inverted image; a screen would need the calculated image plane.

Use 1/f=1/o+1/i with a positive real object distance. A converging/concave element has positive f, a diverging/convex element negative f, and m=−i/o. Mirror positive image distance lies back in front of the mirror, whereas lens positive image distance lies after the lens. The location diagram marks objects and images, not a full ray trace. Paraxial approximation excludes strong off-axis rays, spherical/chromatic aberration and aperture clipping.

Predict before inspecting the values. Save contrasting records with assumptions and one alternative explanation. This virtual display does not certify practical measurement technique.

The model forms a real inverted image; a screen would need the calculated image plane.

Observation to attach to a capture

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

Understand

Define the optical model

Build the signed account

The reciprocal relation remains 1/f=1/o+1/i and transverse magnification is −i/o. Optical power is 1/f only when f is expressed in metres, giving inverse metres, also called dioptres. An object at the positive focal distance produces collimated outgoing rays in the thin-lens approximation; replacing this with a finite screen position hides the model boundary. Changing an arbitrary coordinate origin does not change the distances measured from the lens.

Test the limits and evidence

Three principal-ray rules support a sketch. A ray parallel to the axis emerges through the far focus for a converging lens or along a line whose backward extension reaches the near focus for a diverging lens. A central ray continues undeviated in the ideal thin model. A focal-directed incoming ray emerges parallel: through the incident-side focus for a converging lens, or aimed toward the far-side focus for a diverging lens. These are paraxial rules, not a promise about thick lenses, large angles, colors or aperture clipping.

Worked original case

Predict and investigate

Changed-case practice

Try the changed case before feedback

For a diverging lens with f=−12 cm and a real object at24 cm, find signed image distance in cm.

Numerical result in the requested units

This practice is public and unsaved. A matching number does not verify understanding. Retain your explanation, assumptions and changed-case evidence in the separate course workspace.

Sources and boundaries

Original text and numerical cases checked 30 October 2026 against the primary explanation. All optical activity is virtual: no laser, sunlight viewing, eye exposure, physical lens alignment or device construction is requested. Public feedback is not independent mastery; retain first calculations, critique and changed-case evidence in the separate course workspace.

Apply

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

Which independent observation would reject the approximation, sign convention or calibration premise rather than merely refit it?

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: Classify mirror images before placing a screen Next: Use a signed intermediate object in a two-lens system

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