If the angular magnification of an astronomical telescope is...

If the angular magnification of an astronomical telescope is 36
and the diameter of the objective is $75 \mathrm{mm},$ what is the minimum diameter of the eyepiece required to collect all the light entering the
objective from a distant point source on the telescope axis?

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Key Concepts

Angular Magnification

Angular magnification is the ratio of the angular size of the image produced by an optical instrument to the angular size of the object being observed. In telescope systems, it is typically given by the ratio of the focal length of the objective to that of the eyepiece. This concept is crucial for understanding how much larger a distant object appears when viewed through the telescope.

Exit Pupil

The exit pupil is the image of the telescope’s objective formed by the eyepiece, and it represents the beam of light that exits the instrument. Its diameter, calculated by dividing the objective’s diameter by the angular magnification, is critical because the eyepiece must be large enough to collect the entire exit pupil to ensure that all the light gathered by the objective is transmitted to the viewer.

Optical Aperture and Light Collection

The optical aperture of a system refers to the size of the light-collecting component, usually the objective in a telescope. The ability of the telescope to gather light depends on this aperture size, and proper matching with the eyepiece dimensions, particularly concerning the exit pupil, is necessary to avoid loss of light and to maintain optimal brightness and image quality.

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