Question

Draw a labelled ray diagram of an image formed by a refracting telescope with final image formed at infinity. Derive an expression for its magnifying power with the final image at infinity.

Answer 1

Ray diagram of the image formed at infinity by refracting telescope is shown here which indicates that focal length of objective lens and that of eye piece is $f_o$ and $f_e$ respectively.
Magnifying power of telescope is defined as the ratio of angle subtended by image on eye $\left(\beta \right)$ to angle subtended by object on eye $\left(\alpha \right)$
Magnifying power of telescope $m=-\frac{\beta }{\alpha }$
From figure, $\beta =\tan \beta =\frac{A^{\prime }{B}^{\prime }}{f_e}$
Also, $\alpha =\tan \alpha =\frac{A^{\prime }{B}^{\prime }}{f_o}$
$⟹\frac{\beta }{\alpha }=\frac{f_o}{f_e}$
$⟹m=-\frac{f_o}{f_e}$