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_(o))/(f_(e))and L_(oo)=f_(o)+f_(e)`
`therefore 5=(f_(o))/(f_(e))`….(i)
and 36=`f_(o)+f_(e)`…(ii)
Solving these two equations, we have
`f_(o)=30 cmand f_(e)=6cm`