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_(0)=45 cm` and `f_(e)=-9 cm`
B. `f_(0)50 cm` and `f_(e)=10cm`
C. `f_(0)=7.2 cm` and `f_(e)=5cm`
D. `f_(0)=30cm` and `f_(e)=6cm`.

Answer

D

Explanation

In an astronomical telescope when the object and final image are at infinity, M and L are given as shown:
Angular magnification M`(f_(0))/(f_(e))`
Seperation between lenses, `L=f_(0)=f_(e)`
`,'` `(f_(0))/(f_(0))=5` or `f_(0)=5f_(e)`....(i)
`f_(0)+f_(e)=36` or `5f_(e)+f_(e)=36`
or `f_(e)=6cm`...(ii)
`:'` `f_(0)=5f_(e)` or `f_(0)=30cm`
Hence `f_(0)=30cm`,`f_(e)=6cm`