Why do two elements at the same x behave oddly?

The tracer assumes distinct vertical planes. Separate lens, mirror, and prism positions slightly along the axis.

Is the prism physically accurate?

No — it is a teaching stand-in (constant δ). Real prisms use Snell’s law at two surfaces and wavelength-dependent n.

Optical Bench (sandbox)

A paraxial sandbox on one axis: straight-line segments with slope m = dy/dx. At a thin lens at x, the ray height is continuous and the angle changes by Δθ = −y/f (Gaussian thin lens in air). A vertical plane mirror reverses propagation along x and sends m → −m. A thin wedge is modeled as a constant additive deviation δ on θ at the vertex. Elements are processed in travel order; mirrors can send rays back through upstream optics.

Who it's for: Students who already used the single-lens and two-lens pages and want to compose systems freely.

Key terms

paraxial optics
thin lens
plane mirror
prism
ray tracing

Optical bench (paraxial)

Active elements3

Object x-0.4

Object height0.06

Element 1

Type

x on axis-0.02

focal length f0.2

Element 2

Type

x on axis0.18

Element 3

Type

x on axis0.38

focal length f0.11

Element 4

Type

x on axis0.08

Deviation δ5°

Ideal thin lenses use θ′ = θ − y/f at the vertex; a vertical mirror flips propagation along x and sends y′ = y with slope negated; a thin wedge adds a constant δ to the slope (sign by convention). Rays: yellow = parallel to axis, green = chief toward first bench height on axis, blue = weak third ray.

Shortcuts

Presets place lenses, mirrors, prisms; avoid two elements at the same x
Increase active elements to enable the 4th slot

Measured values

First bench x (chief target)-0.020

Max segments − 1 (bounces)3

How it works

**Sandbox** optical axis: place up to **four** **thin lenses**, **vertical plane mirrors**, or **thin wedges** (constant **δ**). **Paraxial** tracing follows straight segments with **θ → θ − y/f** at each lens, **θ → −θ** at a vertical mirror (light runs backward along **x**), and **θ → θ + δ** at a prism. Compare **two-lens** imaging, a **periscope-style** double bounce, or a **prism** feeding a **lens**.

Key equations

θ′ = θ − y/f (thin lens, small angles)

mirror (vertical): slope m′ = −m · direction along x reverses

wedge: θ′ = θ + δ (toy constant deviation)

Frequently asked questions

Why do two elements at the same x behave oddly?: The tracer assumes distinct vertical planes. Separate lens, mirror, and prism positions slightly along the axis.
Is the prism physically accurate?: No — it is a teaching stand-in (constant δ). Real prisms use Snell’s law at two surfaces and wavelength-dependent n.