Question

An astronomical telescope has an angular Magnification of 40 times. If the diameter of the obejective is 12cm and the length of the tube is 1m, calculate the focal length of the objective and tbe diameter of the exit pupil.

Answer 1

${m=40}\\ {d_{ob}=12cm}\\ {tube\,length=100cm}\\ {calculate\,the\,focal \,length\,of\,the\,objective}\\ {m=\frac{f_o}{f_e}=40}\\ {f_o=40f_e}\\ {tube\,length=f_o+f_e=100}\\ {40f_e+f_e=100}\\ {f_e=2.44cm}\\ {f_o=2.44\times40}\\ {focal\,length\,of\,objective=97.6cm}\\ {diameter\,of\,exit\,pupil}\\ {diameter\,of\,exit\,pupil=\frac{d_{obj}}{m}}\\ {=\frac{12}{40}}\\ {exit\,pupil=0.3cm}$