Thin-lens image location and magnification follow 1/f = 1/do + 1/di and m = −di/do.
University Physics Volume 3 §2.4, Eqs. 2.19 and 2.22, sign conventions and ray rules. Supports real, virtual and infinite-focus cases.
OpenStax · Thin lensesBring light to a meeting point: sources & model
Slide an object toward a lens. Follow the rays, find a sharp image, and discover the moment a camera becomes a magnifier.
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thin-lens-1 · content 1 · setup format 1What supports the explanation?
A camera records a real optical image at a detector plane.
University Physics Volume 3 §2.6, optical focusing and detector discussion. We use the general optical principle, not its dated claims about particular smartphone mechanisms.
OpenStax · The cameraAn eyepiece can magnify by forming a virtual image.
University Physics Volume 3 §2.8, compound microscope explanation. Supports the simple magnifier arrangement; no microscope model is implemented.
OpenStax · Optical instrumentsWhat this model assumes
- Ideal thin lens, paraxial ray construction in air. Distances are from the thin-lens plane. The diagram fits the current setup automatically; it is not life-size.
- Rays represent selected paths of light, not the only light from an object. Animated dots have arbitrary speed and are not photons traveling at the displayed rate.
- Off-screen images are labelled. The camera inset follows an on-axis point separately from the object-arrow image. Its aperture height is enlarged on a different vertical scale to make bundle width visible.
- No eye prescription, solar focusing, laser activity, lens manufacturing or lens aberration model.
- One equation, clear signs: 1/f = 1/do + 1/di. A real object has do > 0. A converging lens has f > 0; a diverging lens has f < 0. A positive di means a real image on the far side. Negative di means a virtual image on the object side.
- Size and orientation: Transverse magnification m = −di/do. Negative m is inverted. At do = f for a converging lens, the emerging bundle is parallel: there is no finite image distance. The calculator reports this explicitly rather than dividing by zero.
- How much misses focus?: For an on-axis point and aperture radius a, the geometric bundle radius at sensor distance s is a|1 − s/di|. The camera inset uses this ray geometry. Diffraction, aberrations, wavelength dependence and real sensor sampling are omitted.
What has been checked
Analytical reference cases, conservation or transition invariants, finite drawing commands, bounded setup parsing, discovery and route integrity are checked automatically. These checks do not establish anatomical fidelity, learner outcomes or browser/device compatibility. Independent subject review, learner trials, comprehensive accessibility review and browser video encoding checks remain pending.
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