| Lesson Plan |
| Grade: |
Date: 25/02/2026 |
| Subject: Physics |
| Lesson Topic: use ∆λ / λ . ∆f / f . v / c for the redshift of electromagnetic radiation from a source moving relative to an observer |
Learning Objective/s:
- Describe the fractional wavelength and frequency shifts and how they relate to the source speed (v / c).
- Apply the non‑relativistic Doppler formula to determine radial velocity from an observed spectral line.
- Analyse a spectroscopic binary’s velocity curve to obtain orbital parameters and estimate stellar masses.
- Use Kepler’s third law and the main‑sequence mass‑radius relation to calculate a star’s radius.
- Evaluate when the full relativistic Doppler expression is required.
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Materials Needed:
- Projector and screen for slides/diagrams
- Handout with laboratory wavelengths (e.g., H‑α 656.28 nm)
- Calculator or spreadsheet software
- Whiteboard and markers
- Worksheet with practice problems on Doppler shift and binary‑star calculations
- Optional: simulation applet showing binary‑star spectra
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Introduction:
Begin with the question “How can we measure the size of a star we cannot see?” Students recall the basic Doppler shift concept and the idea that spectral lines move when a source moves. Explain that by the end of the lesson they will calculate a star’s radial velocity and, using binary‑star dynamics, estimate its radius.
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Lesson Structure:
- Do‑now (5 min): Quick quiz on the sign convention for red‑shift and blue‑shift.
- Mini‑lecture (10 min): Derive the fractional shift equations (Δλ/λ = v/c, Δf/f = ‑v/c) and discuss the non‑relativistic limit.
- Guided example (15 min): Work through a calculation of v from an observed H‑α line shift, highlighting unit conversion.
- Binary‑star activity (20 min): In pairs, use provided data (K, P, i, e) to compute a₁, then apply Kepler’s law and the mass‑radius relation to find the primary’s radius.
- Check for understanding (5 min): Whole‑class discussion of results, common mistakes, and the importance of stating red‑shift vs. blue‑shift.
- Extension (5 min): When to switch to the relativistic Doppler formula and how to convert periods to seconds.
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Conclusion:
Summarise the key equations linking Δλ/λ, Δf/f and v/c and how they enable us to extract stellar radii from binary systems. Exit ticket: each student writes one of the equations and a brief description of its use. For homework, complete the worksheet that extends the binary‑star calculation to a non‑circular orbit.
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