Past exam of the mathematics course of the University of Cambridge 2017 iii Paper 338 2 c i Solution Created 2026-10-03 Updated 2026-10-14
Choose photodetector along increasing main grating dispersion, and along increasing wavelength for the cross-disperser. The echellogram shows two order traces and their intersections with the axis, which passes through the optical camera optical axis.
For fixed incidence, , so increasing wavelength goes to the right along each order. The cross-disperser also sends increasing wavelength upward in the chosen orientation; the traces therefore slope upward. At , , so the trace labeled lies above the trace labeled . Reflecting either plotting axis would reverse its arrow but leave the optical content unchanged. The cross-disperser separates orders that would overlap in the main dispersion direction.
Past exam of the mathematics course of the University of Cambridge 2019 iii Paper 338 1 b i Solution Created 2026-10-03 Updated 2026-10-14
The echellogram contains nearly parallel traces, one for each diffraction order. Choose the main echelle grating dispersion to increase wavelength toward the right and the cross-disperser to increase wavelength upward. At a fixed horizontal coordinate, order has a shorter wavelength than order , so it lies below order in this convention.
Adjacent orders in a cross-dispersed echellogram
. Order m+1 is bluer than order m at the same main-dispersion coordinate. Within either order, wavelength increases along the trace to the right; the chosen cross-dispersion orientation puts longer wavelengths higher on the detector. Details.
