Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2019/iii/paper-338/1/b/i/solution

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.
Figure 1.
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.

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