Saurabh Koranglekar
Last Activity: 5 Years ago
Given:
Minimum angular magnification of an astronomical telescope, M_min = 10X
For an astronomical telescope in normal adjustment (final image at infinity), the angular magnification is given by:
M = f_o / f_e
where:
f_o = focal length of the objective
f_e = focal length of the eyepiece
Since the problem gives M_min, it implies that the telescope has been adjusted for minimum magnification. This occurs when the telescope is in normal adjustment.
Thus, we write:
10 = f_o / f_e
To determine f_o, we need f_e, but it is not given in the problem. However, the minimum magnification of an astronomical telescope is approximately given by:
M_min ≈ D / f_o
where D is the least distance of distinct vision, generally taken as 25 cm.
Rearranging for f_o:
f_o = D / M_min
f_o = 25 cm / 10
f_o = 2.5 cm
Therefore, the focal length of the objective is 2.5 cm.