Question

(a) A giantrefracting telescope at an observatory has an objective lens of focallength 15 m. If an eyepiece of focal length 1.0 cm is used, what isthe angular magnification of the telescope?

(b) If thistelescope is used to view the moon, what is the diameter of the imageof the moon formed by the objective lens? The diameter of the moon is3.48 × 10⁶m, and the radius of lunar orbit is 3.8 × 10⁸m.

Answer 1

Focallength of the objective lens, f_o= 15 m = 15 ×10² cm

Focallength of the eyepiece, f_e= 1.0 cm

(a) Theangular magnification of a telescope is given as:

Hence, the angular magnification of the given refracting telescope is1500.

(b) Diameterof the moon, d= 3.48 ×10⁶ m

Radiusof the lunar orbit, r₀= 3.8 ×10⁸ m

Letbethe 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 anglesubtended by the image.

Hence, the diameter of the moon’s image formed by the objectivelens is 13.74 cm