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, respectively?
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

Given, barrel length of the telescope (L) = 33 cm 
Angular magnification (M) = 10 
Let, distance between objective and eyepiece (d) = x 
Using the formula for angular magnification, 
M = (θ' / θ) = (fₒ / fₑ)
where θ' = angle subtended at the eye by the final image 
and θ = angle subtended at the eye by the object 
fₒ and fₑ are the focal lengths of objective and eyepiece respectively 
Also, total length of telescope, L = fₒ + fₑ 
On substituting the given values, 
10 = (fₒ / fₑ) 
fₒ = 10fₑ 
L = 11fₑ 
33 cm = 11fₑ 
fₑ = 3 cm 
fₒ = 10fₑ = 30 cm 
Therefore, the focal lengths of the objective and the eyepiece are 30 cm and 3 cm, respectively. The correct choice is B.

An Astronomical Telescope Has a Barrel Length of 33 Cm