1. Plate scale
s = 206265/(25.0×1000) = 8.2506 arcsec/mm.
| Criterion | Points |
|---|---|
| Correct formula application | 10 |
| Correct final value | 10 |
Worked Solutions
2. Pixel scale
Pixel scale = 8.2506×0.012 mm = 99.01 milliarcsec/pixel.
| Criterion | Points |
|---|---|
| Correct unit conversion (µm to mm) | 8 |
| Correct final value | 7 |
3. Nyquist check
Half the diffraction-limited FWHM is 23.37 mas; the Problem 2 pixel scale (99.01 mas/pixel) is larger (undersampled) than this Nyquist limit.
| Criterion | Points |
|---|---|
| Correct half-FWHM computation | 8 |
| Correct undersampled/adequate classification | 7 |
4. Design fix
Increasing the focal length to about 105.9 m (proportionally increasing plate scale's denominator) brings the pixel scale down to about 23.37 mas/pixel, adequately sampling the diffraction limit; equivalently, a smaller pixel size at the original focal length would achieve the same result.
| Criterion | Points |
|---|---|
| Correct identification of focal length or pixel size as the lever | 12 |
| Correct resulting numeric pixel scale | 8 |
Grading Notes
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.