ASTR 340 Problem Set 01: Aperture, Collecting Area, and Diffraction-Limited Resolution

Problem set for lecture unit 1.

Problems

1. Collecting area 20 points

Compute Gemini North's collecting area (D=8.1 m) from A=πD²/4, and compute its ratio to Keck's published collecting area (76 m²).

2. Rayleigh criterion at a new wavelength 15 points

Compute Keck's Rayleigh-criterion resolution at H band (1.65 µm) rather than V band, and compare it to Keck's V-band resolution (13.9 mas, Lecture 02/Lab 01).

3. Seeing-limited versus diffraction-limited 15 points

Using the atmospheric seeing floor (0.8″) and your Problem 2 H-band diffraction limit, state whether an uncorrected Keck H-band image would be seeing-limited or diffraction-limited, and justify your answer with the specific ratio.

4. Cassegrain focal-station reasoning 20 points

Explain, using the observing-chain picture from Lecture 01, why an instrument requiring a large, heavy cryostat (e.g., a near-infrared spectrograph) is more often placed at a Nasmyth or Coudé focus than directly at the Cassegrain focus, in terms of the mechanical weight and space constraints at each focal station.

Due and Scope

Submit a complete derivation with equations, units, labeled quantities, and a short narrative interpretation for each problem. Show every step; a correct final number without a visible derivation receives partial credit at most, and quoting a lecture number without adapting it to this problem's specific inputs receives no credit for that step.

OpenStax Companion Reading

OpenStax Astronomy 2e (local reference copy: references/openstax-astronomy-2e-extracted.txt), Chapter 6 (astronomical instruments), descriptive only; this course exceeds that introductory treatment throughout.

References and Data Sources