An astronomical telescope has an angular magnification of magnitude 5 for distant object. The separation between the objective and the eyepiece is 36 cm and the final image is formed at infinity. The focal length `f_(0)` of the objective and the focal length `f_(0)` of the eyepiece are

Options

A. `f_(o) = 45 cm and f_(e) = -9cm`
B. `f_(o) = -7.2 cm and f_(e) = 5 cm`
C. `f_(o) = 50 cm and f_(e) = 10 cm`
D. `f_(o) = 30 cm and f_(e) = 6 cm`

Answer

D

Explanation

In this case, `|m|=(f_(o))/(f_(e ))=5` …..(i)
and length of telescope `= f_(o)+f_(e )=36` …..(ii)
On solving Eqs. (i) and (ii), we get
`f_(e )=6 cm, f_(o)=30 cm`