# Faraday Rotation — Magneto-Optic Effect

Linearly polarized light rotates by β = V·B·L along a magnetic field. Tune B, L and material to see the polarization helix wind, the β-vs-B line, and the nonreciprocal double-pass behind optical isolators.

> Canonical page: https://elysiatools.com/en/visualizations/faraday-rotation

- **Category:** Physics

## Overview

Interactive Faraday rotation (magneto-optic effect) visualization. When linearly polarized light propagates along a magnetic field B through a medium of length L, its polarization plane rotates by β = V·B·L, where V is the material's Verdet constant (rad/(T·m)). Microscopically B makes the medium circularly birefringent (left/right circular eigenwaves travel at different speeds n₊/n₋), so β = π L (n₋−n₊)/λ. The defining NONRECIPROCAL property: the rotation sense is fixed by B, not by the propagation direction, so a round trip adds another +β (total 2β) instead of canceling — this is what powers optical isolators and distinguishes Faraday rotation from reciprocal optical activity (sugar solution, which cancels to 0 on return). Three visualization panels: (1) Main animated scene showing the magnetized medium block (cyan) with the E-field vector (green) rotating steadily along the optical axis, its tip tracing a 3D-projected polarization helix whose total twist is β = VBL; B-field arrows (purple) along the beam; input E-vector (vertical, 0°) and output E-vector (rotated by β) drawn before and after the block with a live rotation arc annotation. (2) Rotation β vs Field B plot showing the strictly linear law (slope V·L), with ghost curves for all five materials (water/crown/flint/TGG/terbium), the 45° isolator reference line, and the live operating point. (3) Nonreciprocal Double-Pass dial comparison showing single-pass (β), Faraday round-trip (2β, nonreciprocal — does not cancel), and reciprocal optical-activity round-trip (0, cancels) as three polarization needles, illustrating the optical-diode principle. Adjustable parameters: magnetic field B (0–5 T), path length L (0–10 cm), wavelength λ (400–700 nm with V ∝ 1/λ² Becquerel scaling so blue rotates more than red), and medium selection from a library of real Verdet constants — Water (V≈1.6), Crown Glass (V≈3.5), Flint Glass (V≈8), TGG Crystal (V≈40, isolator grade), Terbium Glass (V≈75). Five scenario presets: 45° Isolator (TGG tuned to exactly 45°), Glass Block (weak crown-glass rotation), Water Cell (water needs large B·L), Strong TGG, B=0 (no rotation reference). Real-time statistics: rotation β (°), Verdet constant V, round-trip 2β (°), and the B required to reach 45° isolator angle. Educational content covers the Faraday law β=VBL and circular-birefringence mechanism (Faraday 1845), the nonreciprocal optical-diode principle and Faraday isolator design, and applications (interstellar plasma magnetometry via Δβ∝∫nₑB∥dl/λ² mapping Galactic magnetic fields, TGG+NdFeB laser isolators, fiber-optic current/field sensors and gyroscopes, magneto-optical recording, fusion-plasma electron-density diagnostics). Multi-language support (zh, en, es, fr, de, ru, pt).

## Related content

- [Zero-Order Reaction - Interactive Visualization](https://elysiatools.com/en/visualizations/zero-order-reaction): Interactive visualization of zero-order reaction kinetics and concentration changes over time
- [First-Order Reaction - Interactive Visualization](https://elysiatools.com/en/visualizations/first-order-reaction): Interactive visualization of first-order reaction kinetics and exponential concentration decay
- [Second-Order Reaction - Interactive Visualization](https://elysiatools.com/en/visualizations/second-order-reaction): Interactive visualization of second-order reaction kinetics and bimolecular collision dynamics
- [Arrhenius Equation](https://elysiatools.com/en/visualizations/arrhenius-equation): Interactive visualization of temperature effect on reaction rate - Explore activation energy, pre-exponential factor, and rate constant relationship
- [Reversible Reaction](https://elysiatools.com/en/visualizations/reversible-reaction): Interactive visualization of A ⇌ B reversible reaction kinetics - Explore forward and reverse reaction rates, equilibrium constant, and concentration changes over time
- [Consecutive Reaction](https://elysiatools.com/en/visualizations/consecutive-reaction): Interactive visualization of A → B → C consecutive reaction kinetics - Explore intermediate concentration peaks, rate-determining steps, and complete evolution of all species
- [Chain Reaction](https://elysiatools.com/en/visualizations/chain-reaction): Interactive visualization of free radical chain reaction polymerization - Explore initiation, propagation, termination steps, chain growth animation, and molecular weight distribution
- [Le Chatelier's Principle](https://elysiatools.com/en/visualizations/le-chateliers-principle): Interactive visualization of Le Chatelier's Principle - Explore how changes in concentration, pressure, and temperature affect chemical equilibrium with animated molecular dynamics