(a) A giant refracting telescope at an observatory has an objective lens of focal length 15m. If an eyepiece of focal length 1.0cm 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 × 106m, and the radius of lunar orbit is 3.8 × 108m.
Given:
Focal length of the objective lens, fo = 15m = 1500 cm
Focal length of the eyepiece, fe = 1.0 cm
(a) The angular magnification of a telescope is given as:
α = fo × fe
⇒ α = 1500 × 1
⇒ α = 1500
Hence, the angular magnification of the given refracting telescope is 1500.
(b) Diameter of the moon, d = 3.48 × 106 m
Radius of the lunar orbit, r0 = 3.8 × 108 m
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.
The relation between the given variables is,
…(2)
Where,
d = radius of the moon
r0 = radius of lunar orbit or the distance of moon from earth.
d' = 
d′ = 13.74 cm
Hence the diameter of the image of moon formed by telescope is 13.74 cm.