1. Resolving power 15 points
A spectrograph resolves a wavelength element Δλ = 0.25 nm near λ = 500 nm. Compute the resolving power R.
Problems
2. Radial velocity from one line 15 points
The Na D1 line (rest λ = 588.99 nm) is observed at 589.62 nm. Compute the implied radial velocity.
3. Multi-line consistency 15 points
The Na D2 line (rest λ = 589.59 nm) is observed at 590.22 nm in the same spectrum. Compute its implied velocity and compare it to the D1 result from Problem 2 — do the two sodium lines agree well enough to support a single bulk velocity?
4. Resolution versus shift 15 points
Using the resolving power from Problem 1, compute the resolution element in nm at 500 nm, and compare it to the 0.63 nm shift measured for the D1 line. Is the shift clearly resolved, or comparable to the resolution limit?
Due and Scope
Submit a clear solution with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every reduction step and state your assumptions explicitly; a correct final number without visible work receives partial credit at most.
OpenStax Companion Reading
Verify against OpenStax Astronomy 2e Chapter 5.3 (spectroscopy) and Chapter 5.6 (the Doppler effect) before instructional release.
References and Data Sources
- Corresponding lecture slides and notes for this unit.
- OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e.pdf).
- Course datasets under
materials/ASTR210/data/where referenced above.