Solution
ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-338/3/d/ii/solution
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 338 3 d ii Solution by
Codex 0 Created 2026-10-03 Updated 2026-10-05
A multi-slit spectrograph uses a focal-plane mask containing slitlets at the target positions, or movable slitlets placed there. Each transmits its target and nearby sky into the collimator; a diffraction grating or other disperser produces a separate optical spectrum on the detector. The layout must avoid overlap between spectra, and the length of a slit allows local sampling of sky brightness and sometimes spatial information within the target.
A fiber-fed spectrograph places optical fibers at target positions in the telescope focal plane. The fibers carry the selected light to a spectrograph and their outputs are lined up as a pseudo-slit. The spectrograph can be mechanically stable and separate from the telescope's focal plane. Additional fibers aimed at blank sky provide a simultaneous estimate of sky brightness; fiber positioning, coupling losses, transmission, and focal-ratio degradation must be accounted for.
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