An astronomical telescope has a barrel length of 33 cm and an angular magnification of 10.What are the focal lengths of the objective and the eyepiece in that order?
A) 0.3 m, 3 m
B) 30 cm, 3 cm
C) 20 cm,13 cm
D) 3 cm, 30 cm

Question

Quizplus · Accepted Answer

The angular magnification (M) of an astronomical telescope is given by the ratio of the focal length of the objective (f₀) to the focal length of the eyepiece (fₑ) as follows:

M = -f₀ / fₑ

Also, the total length of the telescope (L) is the sum of the focal lengths:

L = f₀ + fₑ

Substituting the given values of L and M, we get:

10 = -f₀ / fₑ
33 cm = f₀ + fₑ

Solving these equations simultaneously, we get:

f₀ = 30 cm
fₑ = 3 cm

Therefore, the best choice is B, which gives the correct focal lengths in centimeters for the objective and the eyepiece, respectively.

An Astronomical Telescope Has a Barrel Length of 33 Cm