An astronomical telescope with a fifteen-fold angular magnification has a tube length of 80 cm. The

Question

An astronomical telescope with a fifteen-fold angular magnification has a tube length of 80 cm. The focal length of the eyepiece is

Professor PC Thomas Classes · Answer

(b) : The length of an astronomical telescope in normal adjustment is $L = f_o + f_e = 80$ cm. The angular magnification is $m = f_o / f_e = 15$, which means $f_o = 15 f_e$. Substituting this into the length equation gives $15 f_e + f_e = 80$ cm, which simplifies to $16 f_e = 80$ cm. Therefore, the focal length of the eyepiece is $f_e = 80 / 16 = 5$ cm.