A refracting telescope has an objective of diameter and focal length

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

Optics and Photonics, Ch Fraunhofer diffraction from apertures and gratings

Problem

A refracting telescope has an objective of diameter Do=80 mmD_o = 80\ \mathrm{mm} and focal length fo=800 mmf_o = 800\ \mathrm{mm}, fitted with an eyepiece of focal length fe=20 mmf_e = 20\ \mathrm{mm}. It is used in light of wavelength λ=550 nm\lambda = 550\ \mathrm{nm}. The observer's eye pupil is 5.0 mm5.0\ \mathrm{mm} in diameter. ((a)) Using the angular magnification M=fo/feM = f_o/f_e, find the diameter of the exit pupil (the image of the objective formed by the eyepiece). ((b)) Find the smallest angular separation of two point stars that this telescope can resolve. ((c)) State, in one sentence, whether swapping to a much shorter-focal-length eyepiece (say fe=4 mmf_e = 4\ \mathrm{mm}) would change your answer to part (b), and why.

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