Aperture, Collecting Area, and Diffraction-Limited Resolution
A_Gemini = π(8.1)²/4 = 51.5 m². Ratio to Keck: 0.678 -- Gemini North's collecting area is somewhat smaller than Keck's, consistent with its slightly smaller 8.1 m aperture.
| Criterion | Points |
|---|---|
| Correct area arithmetic | 10 |
| Correct ratio and direction | 10 |
θ_H = 1.22×1.65µm/10m = 41.5 mas, coarser than the V-band value (13.9 mas), consistent with the direct proportionality of resolution to wavelength.
| Criterion | Points |
|---|---|
| Correct arithmetic | 10 |
| Correct direction (coarser at longer wavelength) | 5 |
Ratio = 0.8″/0.0415″ = 19 -- still far larger than 1, so an uncorrected Keck H-band image remains strongly seeing-limited, not diffraction-limited, even though the gap is smaller than at V band.
| Criterion | Points |
|---|---|
| Correct ratio | 8 |
| Correct seeing-limited conclusion | 7 |
The Cassegrain focus is compact but mass- and space-constrained (it moves with the telescope through its full range of motion); Nasmyth and Coudé foci route light to a stationary or slower-moving platform with far more room and weight capacity for large cryostats, optical benches, and vibration-sensitive components, which is why the heaviest instruments are placed there rather than at Cassegrain.
| Criterion | Points |
|---|---|
| Correct identification of the weight/space trade-off | 12 |
| Correct connection to instrument type | 8 |
Award full marks for correct method, units, and a numeric result consistent with the arithmetic shown (allow reasonable rounding). Verify that the student re-derives the number for this problem's specific inputs rather than quoting a lecture example without adaptation. Watch specifically for unit-conversion errors (arcsec/radian, nm/m, mm/m) and for comparative-magnitude or comparative-resolution statements given in the wrong direction (e.g., "finer" versus "coarser" resolution, or "more" versus "less" light-gathering power) -- these are the most common sources of order-of-magnitude mistakes in this course.