I am solving an optics exercise that requires to design a Keplerian telescope with a given magnification M (negative), a certain object size L and the restriction of not having lenses faster than F/1 (wavelength of the signal and resolution are also given, but they are used for solve successive questions). In particular, the exercise requires to retrieve the NA of the objective lens from the optical invariant of the system.

Given these information, I would say that, using the fastest lenses possible, I would need a first lens with radius R1=L and a focal length of F1=2L (so that the F/1 requirement is satisfied), while the second lens should have a focal length of F2=|M|F1, a distance from the first of d=F1+F2 and a radius of R2=|M|L. However, I am not sure how to retrieve the Lagrange invariant (https://en.wikipedia.org/wiki/Lagrange_invariant) from this theoretical design: for once, since the system is afocal, the object should be at infinity, thus how can the marginal ray be defined? Moreover, in this case both the first and the second lens limit the marginal rays of the system, and being the object at infinity I am not sure how should it be tilted (shouldn't it be parallel to the optical axis? But then wouldn't it coincide with the chief ray?).


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