---
title: "Why a magnetic field splits a spectral line"
description: "How did the lines Zeeman observed and the polarization Lorentz predicted support the same explanation?"
canonical_url: "https://sandboxphysics.com/stories/quantum-evidence/zeeman-lines-polarization-lorentz/"
language: "en"
page_type: "story"
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  zh-CN: "https://sandboxphysics.com/zh/stories/quantum-evidence/zeeman-lines-polarization-lorentz/"
last_modified: "2026-10-24"
---

[Quantum physics: reading the evidence](https://sandboxphysics.com/stories/quantum-evidence/)

Nobel A · Evidence and control

# Why a magnetic field splits a spectral line

Sandbox Physics · 2026-10-15

How did the lines Zeeman observed and the polarization Lorentz predicted support the same explanation?

## Put the source between the magnet poles

Spread the light from a glowing substance into its colours and bright, narrow lines appear. Each line marks a particular colour emitted by the substance. In Leiden in 1896, Pieter Zeeman investigated whether a magnetic field could change them. He placed the source between magnet poles and compared its spectrum with the field on and off. At first, the striking change was a broadening of a narrow line.

The change happened where the light was emitted. The magnetic field affected motion inside the source. Zeeman described the observation in his 1897 report and sought an explanation from Hendrik Lorentz. The experiment and the theory would share the 1902 Nobel Prize in Physics.

Read the evidence: P. Zeeman (1897), The Effect of Magnetisation on the Nature of Light Emitted by a Substance, Nature 55, 347 P. Zeeman (1897), original Nature report — University of Maryland scan Nobel Prize in Physics 1902 — official award record

## The direction of the light mattered

Broadening alone left several possibilities. Hotter atoms move faster; collisions also disturb the emission of light. Lorentz offered a more specific prediction. In his account, a magnetic field changed the frequencies of a charged oscillator differently for different directions of vibration. Colours that had overlapped could separate.

The direction in which light vibrates is its polarization. Looking along the magnetic field, Lorentz predicted opposite circular polarizations at the two edges of the broadened line. In circularly polarized light, the vibration direction rotates around the direction of travel. A view across the field should give a different set of polarized components. Zeeman tested these predictions, connecting the spectrum to both the viewing direction and the light’s vibration.

The familiar ideal normal triplet makes that connection easy to picture. Viewed across the field, it has a central component polarized parallel to the field and two shifted components polarized perpendicular to it. Viewed along the field, the central component is absent and the two outer components are circularly polarized. Changing the viewing direction changes which components reach the observer.

Read the evidence: P. Zeeman (1897), The Effect of Magnetisation on the Nature of Light Emitted by a Substance, Nature 55, 347 P. Zeeman (1903), Light Radiation in a Magnetic Field — Nobel lecture, University of Maryland copy NIST Atomic Spectroscopy, Zeeman Effect — weak-field energy shifts and magnetic factors

## The modern account starts with atomic energies

An atom can have only certain energies, called energy levels. When it drops from a higher level to a lower one, it releases the energy difference as light. A magnetic field shifts those levels. Transitions that once had the same energy can then emit slightly different colours.

The equation gives the shift of one magnetic sublevel in a weak field. B is the magnetic field, the Bohr magneton converts field into energy, and the magnetic factor and projection label describe the state’s magnetic response. The shift of a spectral line depends on the changes at both ends of its transition. This weak-field expression assumes the original angular-momentum labels still describe the states.

$$
\Delta E=g_J\mu_{\mathrm B}m_J B
$$

Read the evidence: NIST Atomic Spectroscopy, Zeeman Effect — weak-field energy shifts and magnetic factors

## A success for classical theory, then a harder puzzle

Lorentz’s classical charged oscillator explained the simplest normal triplet remarkably well. His success tied the field to both the colours and their polarizations. That achievement belongs in the story before the later quantum explanation.

More complicated splitting patterns eventually required additional atomic structure, including electron spin. Stronger fields can also change how the atom’s internal motions couple, beyond the linear weak-field formula. The original experimental lesson remains accessible: ask how far a colour moves, then ask how the light vibrates and from which direction it is being observed.

Read the evidence: P. Zeeman (1903), Light Radiation in a Magnetic Field — Nobel lecture, University of Maryland copy Nobel Prize in Physics 1902 — official award record NIST Atomic Spectroscopy, Zeeman Effect — weak-field energy shifts and magnetic factors

## Continue with the models

These teaching Labs produce simulated data, which are separate from the historical observations discussed above.

- [Count the polarized components of a normal Zeeman line](https://sandboxphysics.com/labs/zeeman-polarization-spectrometer/)
- [See how levels and line strengths change with the field](https://sandboxphysics.com/labs/coupled-spin-spectroscopy/)

## Sources and reading notes

We link the 1897 Nature report and a University of Maryland scan of it; its text reports the broadening and Lorentz’s prediction of polarization. A university copy of Zeeman’s Nobel lecture of May 1903 gives his own look back at sodium broadening and the cadmium triplets. The modern weak-field formula comes from NIST. We do not reanalyze any historical plate.

1. [P. Zeeman (1897), The Effect of Magnetisation on the Nature of Light Emitted by a Substance, Nature 55, 347](https://www.nature.com/articles/055347a0)
2. [P. Zeeman (1897), original Nature report — University of Maryland scan](https://physics.umd.edu/grt/taj/623e/Zeeman1897.pdf)
3. [NIST Atomic Spectroscopy, Zeeman Effect — weak-field energy shifts and magnetic factors](https://www.nist.gov/pml/atomic-spectroscopy-compendium-basic-ideas-notation-data-and-formulas/atomic-spectroscopy-zeeman)
4. [Nobel Prize in Physics 1902 — official award record](https://www.nobelprize.org/prizes/physics/1902/summary/)
5. [P. Zeeman (1903), Light Radiation in a Magnetic Field — Nobel lecture, University of Maryland copy](https://physics.umd.edu/grt/taj/623f/Pieter%20Zeeman%20-%20Nobel%20Lecture-%20Light%20Radiation%20in%20a%20Magnetic%20Field.pdf)

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