= Solution
A <classical Schmidt telescope> combines a concave spherical primary with a thin aspheric corrector plate at its centre of curvature. The plate is also near the aperture stop. It supplies just the extra ray bending needed to cancel the mirror’s <spherical aberration>; rays then return toward an internal focus roughly halfway between the plate and primary. The native best-focus surface is curved, as indicated in red.
\Image[/past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2018/iii/paper-338-schmidt.png]
{title=Light paths in a Schmidt telescope}
The spherical primary is easy to manufacture, and the stop at its centre of curvature gives a nearly symmetric optical geometry that suppresses <coma> and <astigmatism> over a large field. Fast <Schmidt cameras> are consequently excellent survey instruments. The costs are a long enclosed optical assembly, a large precision corrector, an internal camera that obstructs the beam, and a curved focal surface. A flat detector needs field flattening. The transmissive corrector introduces wavelength-dependent effects and transmission losses, unlike an entirely reflecting system.
\b[Spherical primary + aspheric corrector at the centre of curvature → wide field on a curved internal focal surface.]
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