Question

(a) A giant refracting telescope at an observatory has an objective lens of focal length $15m$. If an eyepiece of focal length $1.0$ cm is used, what is the angular magnification of the telescope?
(b) If this telescope is used to view the moon, what is the diameter of the image of the moon formed by the objective lens? The diameter of the moon is $3.48\times {10}^{6}m$, and the radius of lunar orbit is $3.8\times {10}^{8}m$.

Answer 1

(a) Angular magnification of a telescope is

$m=\frac{f_o}{f_e}$

$=\frac{15}{0.01}$

$=1500$

(b) Let $d$ be diameter of moon and $r_o$ be radius of lunar orbit.

Let $d^{{}^{\prime }}$ be the diameter of image of moon.

The angle subtended by the diameter of the moon is equal to the angle subtended by the image.

$\frac{d}{r_o}=\frac{d^{{}^{\prime }}}{f_o}\Rightarrow d^{{}^{\prime }}=13.74cm$