9.14: (a) A giant refracting telescope at an observatory has an objective lens of focal length 15 m. 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 x 106 m, and the radius of the lunar orbit is 3.8 x 108m.

(a)
Hint: \(\alpha =\frac{f_{0}}{f_{e}}\)

Step: Find the angular magnification of a telescope.
Focal length of the objective lens, fo=15 m = 15 x 102 cm and focal length of the eyepiece, fe = 1.0 cm
The angular magnification of a telescope is given by:

α=ffe=15×1021.0=1500

(b)
Hint:
The angle subtended by the diameter of the moon is equal to the angle subtended by the image of the moon.

Step: Find the diameter of the image of the moon.
Let d’ be the diameter of the image of the moon formed by the objective lens.
The angle subtended by the diameter of the moon is equal to the angle subtended by the image of the moon.
\(tan\theta =\frac{d}{r_{0}}=\frac{d^{'}}{f_{0}}\\\Rightarrow \frac{3.48\times10^{6}}{3.8\times10^{8}}=\frac{d^{'}}{15}\\\therefore d^{'}=13.74 cm\)