# Polarization Simulator - Jones Calculus, Wave Plates, Brewster Angle, Photoelasticity

> Jones-calculus optical bench: drag polarizers and wave plates, see the E-field ellipse and Poincaré sphere; Brewster angle, calcite, interference colors, LCDs.

- URL: https://qilingtools.com/en/physics/polarization
- Category: Physics Tools (https://qilingtools.com/en/physics)
- Tags: [Physics](https://qilingtools.com/en/tags/physics), [Education](https://qilingtools.com/en/tags/education)
- Last updated: 2026-10-29
- Price: Free, no sign-up
- Privacy: Runs locally in the browser; files are never uploaded

Line up polarizers, quarter-wave and half-wave plates and rotators, drag the discs to rotate them, and watch the electric-field ellipse, transmitted intensity and Poincaré-sphere position after every stage. Other pages cover glare and polarized sunglasses, the calcite double image and interference colors of thin plates (real colors from CIE color-matching functions), photoelastic fringes in a loaded disk and beam, and how LCD pixels and 3D cinema glasses work.

## How to use

1. Pick a preset (such as the three-polarizer paradox) or choose a source and add polarizers and wave plates
2. Drag the discs in the top row to rotate elements and watch the field ellipse and intensity after each stage
3. Use the sweep chart to see output vs one element’s angle, and the Poincaré sphere to see how the state moves
4. Switch to the reflection, birefringence, photoelasticity and LCD pages and change parameters to see colors and fringes respond

## Features

- Jones matrices plus coherency matrices, so natural, partially polarized and any elliptical light work
- Animated field vector with handedness, azimuth, ellipticity and degree of polarization per stage
- Draggable Poincaré sphere: wave plates rotate the state, polarizers project it
- Fresnel reflectances, Brewster angle and polarized-sunglasses glare reduction
- Calcite walk-off and double image, Michel-Lévy chart, photoelastic isochromatics and isoclinics
- Layered Jones model of a TN liquid-crystal cell and 3D-glasses crosstalk comparison

## FAQ

### Why does adding a third polarizer between crossed polarizers let light through?

After the first polarizer the light is linear at 0°; a 90° polarizer passes cos²90° = 0, so it is dark. Insert a 45° polarizer in between and the light passes with cos²45° = 1/2 and becomes 45° polarized, then passes the last one with another 1/2. Natural light gets through at 1/2 × 1/2 × 1/2 = 12.5%. A polarizer is not a sieve: it projects the field onto its axis and resets the polarization direction.

### How does a quarter-wave plate turn linear into circular polarization?

The plate has different indices along its fast and slow axes, so the two components come out 90° apart in phase. With the input at 45° to the fast axis the two components are equal, and a 90° phase lag makes the field tip trace a circle. At other angles the components differ and the result is elliptical. On the Poincaré sphere it is a 90° rotation about the fast-axis direction.

### Why do polarized sunglasses cut glare from water?

On reflection the s component (parallel to the surface) reflects much more than the p component in the plane of incidence, and at Brewster’s angle (about 53° for water) p is not reflected at all, so glare is mostly horizontally polarized. Polarized lenses transmit vertical polarization and block it. The tool shows how much glare is removed at each angle and how tilting your head weakens the effect.

### Where do the colors of rock thin sections in crossed polars come from?

A birefringent plate delays one polarization by Γ = Δn·t. Between crossed polarizers the transmission at wavelength λ is sin²(πΓ/λ), so some wavelengths are removed and others enhanced, and the remaining spectrum mixes into an interference color. The tool integrates that spectrum with the D65 illuminant and CIE 1931 color-matching functions and draws the Michel-Lévy chart: in a standard 30 µm section quartz shows first-order gray-white and calcite high-order white.

### What do photoelastic fringes show?

Loaded transparent plastic becomes temporarily birefringent, with retardation proportional to the principal-stress difference: Γ = C·t·(σ₁−σ₂). In a circular dark-field polariscope each colored fringe is a line of constant σ₁−σ₂ (an isochromatic), and closely spaced fringes mean steep stress gradients. A plane polariscope also shows black isoclinics where a principal direction lines up with the polarizer. The tool uses closed-form elasticity solutions for a disk in diametral compression and a simply supported beam.

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