Q: An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and eye piece is 36 cm and the final image is formed at infinity. Determine the focal length of objective and eye piece.

Sol: For final image at infinity,

$\large M = \frac{f_o}{f_e} $

$\large 5 = \frac{f_o}{f_e} $ …(i)

And , L = f_{0} + f_{e}

36 = f_{o} + f_{e} …(ii)

Solving these two equations, we have

f_{o} = 30 cm and f_{e} = 6 cm