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How does the James Webb Space Telescope achieve a focal length of 131.4m ?

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The JWST has three mirrors(*), the main mirror (6.5m in diameter) A secondary mirror, held on three struts in front of the main mirror and a tertiary mirror that reflects the light into the various instruments.

The length of the light path from Main mirror to focal point is about 20m, but this is not the focal length, since the secondary mirror is convex, the tertiary mirror is also curved to remove the astigmatism caused by the secondary being slightly off-centre. The convex curvature on the secondary has a "telephoto" effect, lengthening the effective focal length.

The convex secondary mirror gives an effective focal length of 131.4m. The three mirrors together function as if the telescope had a single mirror with focal length 131.4m. This layout is called a "Cassegrain" telescope, and is popular both for billion-dollar telescopes and amateur instruments. It allows for a much longer focal length to fit in a short stable package. Both Hubble and the VST are also Cassegrain telescopes.

Here is an animation to show how light is collected by the mirrors.

(*) It actually has lots more, but to understand the focal length there are effectively three.

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    $\begingroup$ yes, okay, but the 20 hexagonal ones act as one mirror $\endgroup$
    – James K
    Commented Nov 6, 2022 at 6:10
  • $\begingroup$ it's three mirrors to some primary focus for which the focal length is quoted, but I think any light reaching an actual detector or image sensor sees more like eight or ten reflections in total NIRISS and MIRI and NIRCAM $\endgroup$
    – uhoh
    Commented Nov 6, 2022 at 7:03
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    $\begingroup$ Yes, but that is, in the context of the question, an engineering detail. It is the cassegrain construction with a convex secondary that gives an effective focal length longer than the light path length. $\endgroup$
    – James K
    Commented Nov 6, 2022 at 7:13
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    $\begingroup$ @LeosOndra very carefully curved. See the figure here webb.nasa.gov/content/observatory/ote/mirrors/index.html three curvatures labeled "A", "B" and "C" are used to make a very specific shape. It's a 3-mirror anistigmat or Korsch design $\endgroup$
    – uhoh
    Commented Nov 6, 2022 at 8:17
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    $\begingroup$ @JamesK it turns out it's not Cassegrain; it's a three Mirror Anastigmat orKorsch design. $\endgroup$
    – uhoh
    Commented Nov 6, 2022 at 8:26

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