= Solution
Choose <photodetector> $x$ along increasing main <grating dispersion>, and $y$ along increasing <wavelength> for the <cross-disperser>. The <echellogram> shows two order traces and their intersections with the $y$ axis, which passes through the <optical camera> <optical axis>.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2017/iii/paper-338-echellogram.png]
{title=Two adjacent cross-dispersed echelle orders}
For fixed incidence, $d\beta/d\lambda=m/(d\cos\beta)>0$, 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 $x=0$, $\lambda_m=K/m>\lambda_{m+1}=K/(m+1)$, so the trace labeled $m$ lies above the trace labeled $m+1$. Reflecting either plotting axis would reverse its arrow but leave the optical content unchanged. \b[The cross-disperser separates orders that would overlap in the main dispersion direction.]
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