Wiki / Lenses / Convex lens

Convex lens

Bends rays with a thin-lens, paraxial focal-length model.

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In the real world

A thin lens bends light by refraction at its two curved surfaces. In the paraxial approximation — rays close to the optical axis, at small angles — those two refractions collapse into a single relationship between object distance dₒ, image distance dᵢ, and focal length f:

1f=1do+1di\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}
The thin-lens equation.
m=didom = -\frac{d_i}{d_o}
Transverse magnification — negative sign means an inverted image for a real image from a positive lens.

In OpticalSetup

Rather than tracing the thin-lens equation for one axial object point at a time, OpticalSetup applies the equivalent paraxial ray-transfer relation to every individual ray that crosses the lens plane. For a ray crossing at height h from the optical axis with incoming slope u (the ratio of its transverse to axial direction components), the outgoing slope is:

u=uhfu' = u - \frac{h}{f}
Paraxial ray-transfer equation for a thin lens — the same physics as the lens equation above, applied per-ray so any bundle of rays (not just one object point) focuses correctly.
Simplified vs. reality

This is genuine paraxial optics, not a hand-wavy "bend toward focus": a beam of parallel rays offset from the axis really does converge at the back focal point, and an object arrow really does form an inverted, magnified, or demagnified image at the position the lens equation predicts. What's missing is everything paraxial theory leaves out by construction — spherical and chromatic aberration, finite lens thickness, and any behavior for rays far from the axis or at large angles.

Related components

Further reading