Question

If the angular magnification of an astronomical telescope is 33 and the diameter of the objective is 60 mm, what is the minimum diameter of the eyepiece required to collect all the light entering the objective from a distant point source located on the telescope axis?

Answer 1

You need to think in terms of the entrance & exit pupils of the telescope, these are, respectively, the aperture of the objective (60mm diameter in this case), and the image of this aperture as formed by the eyepiece. The ratio of the diameters of the two pupils is the magnification of the telescope. So we can write 33 = 60/d where d is the diameter of the exit pupil. This gives d = 1.82mm.

The diameter of the eyepiece lens should be at least as great as that of the exit pupil if the conditions described in the question to be realized, so the answer to the question is 1.82mm.