Doppler Shift of Light

draft readiness: candidate LightSpectra DataInference Both 14 min

Active development: draft / candidate

SoTA UX/pedagogy uplift is complete (playbar transport, deeper challenge deck, tooltip affordances, cross-demo scaffolding) and automated gates are passing; launch-ready now depends on classroom and screen-reader validation artifacts.

Launch demo Open fullscreen Station card Instructor notes

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Predict

Hydrogen H-alpha sits at 656.3 nm. If a source is approaching at 300 km/s, does the line move to longer or shorter wavelength, and by about how much?

Play

Start at rest, identify the representative line in both lab and observed strips.
Set +300 km/s and then -300 km/s. Compare direction changes in both wavelength and frequency readouts.
Switch to relativistic mode and apply preset 7 (3C 273) and preset 8 (high-z galaxy).
Use the redshift-slider regime markers and divergence readout to identify where non-relativistic error exceeds 5%.
Open the Sound vs Light callout and explain why observer-side crest spacing is uniform for light.
Use the `Why this line?` helper to verify how representative-line anchoring works.
Run one Mystery Spectrum round: predict -> check -> explain your evidence, then copy challenge evidence for debrief.

Explain

At what velocity scale does the non-relativistic Doppler formula become meaningfully wrong (>5% error), and why does the approximation break there?

Learning goals

Relate radial motion to observed wavelength and frequency shifts in spectral lines.
Interpret redshift z and convert between z and radial velocity with the correct formula.
Decide when non-relativistic Doppler is acceptable and when relativistic Doppler is required.
Use lab-vs-observed spectral comparisons to infer motion direction and speed.

Misconceptions targeted

Light waves should bunch near the source like sound ripples in air.
Redshift always means cosmological expansion; all redshifts are the same mechanism.
Wavelength and frequency shifts are perfectly symmetric at any speed in non-rel formulas.

Model notes

Kinematic Doppler model for light only: positive velocity means receding (redshift), negative means approaching (blueshift).
Physical state coupling uses relativistic conversion between z and v_r; formula toggle changes readout prediction mode, not physical state storage.
When non-relativistic error exceeds 5% (relativistic regime), the demo applies relativistic predictions and announces the fallback.
The redshift slider includes two marker thresholds (blue and red) for the 5% approximation boundary because $z$ mapping is asymmetric.
Wave diagram shows uniform observer-side crest spacing at $\lambda_{\rm obs}$; this is intentional misconception resistance against sound-style ripple intuition.
Non-relativistic formulas: lambda_obs = lambda_0 (1 + v/c) and nu_obs = nu_0 / (1 + v/c); note the finite-v asymmetry.
Relativistic formulas: lambda_obs = lambda_0 sqrt((1+beta)/(1-beta)) and nu_obs = nu_0 sqrt((1-beta)/(1+beta)).
Regime classification uses divergence between z_nonrel and z_rel to quantify approximation quality.
Representative-line readouts use the strongest visible rest line (380-750 nm) when available, while all catalog lines still shift in the comparator.
The representative-line helper chip explains visible-first anchoring and fallback to strongest-overall line when no visible line exists.
Mystery mode includes a post-check evidence copy helper without changing `ExportPayloadV1` Copy Results behavior.
Hydrogen wavelengths are model-derived; multi-element catalogs are empirical line lists (vacuum wavelengths, NIST teaching subset).
Cosmological and gravitational redshift are distinct mechanisms and not modeled in this instrument.

About this demo

Explore how relative motion shifts spectral lines and why astronomers can measure radial velocity from light alone.