Required lab「Convex lens imaging」: thin-lens equation 1/u+1/v=1/f, three principal rays, five imaging regions and the f / 2f boundaries. On a realistic 3D optical bench, move object and screen independently; check v, |m|, and everyday uses (camera, projector, magnifier).
Memory cue: u > 2f reduced real · f < u < 2f enlarged real · u < f enlarged virtual. Boundaries at 2f (size) and f (real/virtual).
Key formulas
1/u + 1/v = 1/f
m = −v/u = h′/h
How to use
1Read Start here and Related knowledge; skim the mind map first.
2On the 3D optical bench, run the demo far → near across five regions.
3For real images, align the screen (or Align screen) and check v, |m|; for virtual images, look through the lens. Rays refract only if they hit the glass.
Read next
Related knowledge
Read concepts → rays & formulas → lab & five cases → applications & the eye — and check far → near on the 3D optical bench.
Mind map
1. Core ideas
A lens bends light by refraction because its thickness varies. This lab focuses on the convex lens.
Convex lens: thicker in the middle; converges light.
Concave lens: thinner in the middle; diverges light (used to correct myopia).
Optical axis: the line through the two centers of curvature.
Optical center O: a ray through O is undeviated.
Foci F / F′: where rays parallel to the axis meet after the lens (or their extensions).
Focal length f = OF; smaller f means stronger converging (or diverging) power.
Coaxial setup: keep object, lens center, and screen center at one height.
2. Three principal rays
From the object tip, draw these rays; a real image is where rays meet, a virtual image where backward extensions meet.
Parallel to the axis → through F′ after refraction.
Through O → continues undeviated in a straight line.
Through F → emerges parallel to the axis.
3. Lens formulas
1/u + 1/v = 1/fThin-lens equation: object u, image v, focal length f (v < 0 for same-side virtual images).
m = −v/u = h′/hLateral magnification: |m| is size; minus usually means inverted (real), plus upright (virtual).
4. Core lab procedure
Goal: relate object distance to whether the image is real/virtual, larger/smaller, upright/inverted. Typical kit: candle, convex lens, screen, optical bench, matches, ruler.
Assemble and align: flame, lens center, and screen center at one height.
Change u from far to near; for each u, move the screen until sharp; record u, v, and image traits.
When u < f, the screen cannot catch the image — look through the lens for the virtual image.
5. Five cases (far → near)
Match each case to f / 2f: image traits + where v lies + a typical application.
u > 2f: inverted, reduced, real; f < v < 2f → camera.
u = 2f: inverted, same size, real; v = 2f → useful for measuring f.
f < u < 2f: inverted, enlarged, real; v > 2f → projector / slide.
u = f: no image (exit rays parallel) → parallel-beam idea.
u < f: upright, enlarged, virtual; same side, not on a screen → magnifier.
6. Key laws & boundaries
At 2f: boundary between reduced and enlarged; same-size real image.
At f: real/virtual (and inverted/upright) boundary; no image forms.
Real images: object closer → image farther → image larger.
Real: converging rays; inverted; can be caught on a screen; opposite side from the object.
Virtual: backward extensions meet; upright; cannot be caught on a screen; same side as the object.
In this sim: dashed orange lines are extensions, not real light paths.
8. Everyday applications
Camera: convex lens, u > 2f → inverted reduced real image (sensor ≈ screen).
Projector / slide: f < u < 2f → inverted enlarged real image (mirrors often redirect).
Magnifier: u < f → upright enlarged virtual image.
Microscope: two convex lenses — objective forms an inverted enlarged real image; eyepiece forms an upright enlarged virtual image.
Telescope: two convex lenses — objective forms an inverted reduced real image; eyepiece forms an upright enlarged virtual image.
9. Eye & glasses
Eye: crystalline lens ≈ convex lens, retina ≈ screen; a distant object forms an inverted reduced real image.
Myopia: lens too strong or eyeball too long — image in front of the retina; correct with a concave (diverging) lens.
Hyperopia: lens too weak or eyeball too short — image behind the retina; correct with a convex (converging) lens.
Diopters ≈ 100/f (f in metres); positive for convex, negative for concave.
10. Extensions & pitfalls
Extension: lens imaging rests on refraction; persistence of vision (~0.1 s) underlies continuous film frames.
No image is not always a failure: at u = f there is none; for u < f look through the lens, not only at the screen.
A screen catches only real images; virtual images stay on the object’s side.
Enlarged/reduced is relative to the object; beyond 2f the real image is smaller than the object.
Measure u and v from the optical center; the screen is sharp only at the convergence plane.
11. Practice in this sim
Run the guided demo far → near through all five regions first.
Use region presets or the object slider; for real images, move the screen to the ray tip (or Align screen).
Check v and |m| against the formulas; for virtual images, find the extension tip — then connect to the eye, glasses, and everyday uses.
Applications
Cameras, projectors, and magnifiers map to different object-distance regimes.
The eye’s lens behaves like a convex lens that adjusts focus.
FAQ
What if the object is inside the focal length?
An upright, enlarged virtual image on the same side — not on a screen; look through the lens (magnifier).
Why no image when u = f?
f is the real/virtual boundary: refracted rays leave parallel and never meet on a screen.
Why is u = 2f special?
2f is the reduced/enlarged boundary: inverted same-size real image with v = 2f.
What if the screen image is blurry?
A real image is sharp only when the screen sits at the image plane. Drag the screen or use Align screen.
What does “some rays miss the lens” mean?
The lens has a finite aperture: construction rays refract only if they hit the glass; otherwise they go straight. Lower object height slightly, or check which principal rays are enabled.
What happens when u = f?
No finite image — rays leave parallel (image at infinity).
Real vs virtual image?
Real images are inverted and screen-catchable; virtual are upright.
