§ 16 · Optical bench · Lens — Mirror — Screen Filed 2026.05

Drag a lens. Watch a real image form.

An optical bench in your browser. Pick up light sources, lenses, mirrors and screens; slide them along the axis; rays bend, focus, and re-form on the other side. The thin-lens equation and the law of reflection are the only rules — everything else is geometry. Build a telescope, build a microscope, and see why your magnifying glass flips the world at arm's length.

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Bench

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Layout—

Object distance · u—

Image distance · v—

Magnification · M—

How the bench thinks

§ 16 · Notes

Rays

Each light source emits a fan of paraxial rays. A ray is just a pair: a height y above the optical axis and a slope θ. Free flight along the axis carries y forward by θ·d and leaves θ alone.

Lens

A thin lens transforms a ray the simplest possible way: height is unchanged, slope picks up −y/f. Positive f means converging (convex); negative means diverging (concave). Everything you've ever heard about lenses falls out of that one line.

Mirror

A flat mirror reverses the direction of travel; a concave mirror does that and applies −y/f with f = R/2. After bouncing, the ray walks back through whatever it came through, in reverse order.

Image

Rays leaving the same point on an object cross again at a single point on the image — that's what a sharp lens does. The bench finds that crossing, marks it, and reports u, v, and the magnification M = −v/u.

Telescope

Two convex lenses whose focal points coincide. Parallel rays from a distant star enter the objective, focus at the joint focal plane, then exit the eyepiece parallel again — magnified by f_obj/f_eye.

Microscope

A short-focus objective casts a real, enlarged image just inside the eyepiece's focal length. The eyepiece then magnifies that image like a hand lens. Two stages of magnification, multiplied.