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

Explanation

For final image at infinity,
`M_(oo)=f_(0)/f_(e)` and `L_(oo)=f_(0) + f_(e)` `:. 5=f_(0)/f_(e)to(1)`
and `36=f_(0)+f_(e)to (ii)`
Solving these two equiations, we have
`f_(0)=30cm` and `f_(e)=6cm`