Question

If the angular magnification of an astronomical telescope is 26 and the diameter of the objective is 76 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

This is a question about the exit pupil of the telescope.

"For a telescope, the diameter of the exit pupil can be calculated by dividing the focal length of the eyepiece by the focal ratio (f-number) of the telescope. More simply, it is the diameter of the objective lens divided by the magnification." (see link below).

The diameter of the lens in a simple eyepiece must be at least the diameter of the exit pupil if light entering the objective parallel to the axis is not to be lost.

So the answer to your question is that the diameter must be at least 76/26 = 2.11 mm