An afocal telescope with an objective of diameter and angular magnification delivers…

PHYSICS · Multi-part · Fermi University Physics · Optics & Photonics · Geometrical optics and imaging · Geometrical optics and imaging

What an Instrument Can See, Ch The paraxial system as an operator

Problem

An afocal telescope with an objective of diameter

80\ \mathrm{mm}

and angular magnification

10\times

delivers an emerging exit beam of diameter

8\ \mathrm{mm}

, consistent with the Lagrange invariant applied at the objective and at the exit beam. A designer wants a compact version with an objective diameter of

60\ \mathrm{mm}

and magnification

15\times

, and specifies an exit beam diameter of

5\ \mathrm{mm}

. ((a)) Use the Lagrange invariant to find the exit beam diameter that a

60\ \mathrm{mm}

objective at

15\times

magnification actually delivers. ((b)) State whether the designer's specification of a

5\ \mathrm{mm}

exit beam is achievable with this objective and magnification, and if not, find the magnification that would give a

5\ \mathrm{mm}

exit beam with the same

60\ \mathrm{mm}

objective.

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