Question

If length of astronomical telescope is $80$cm and its magnification is $15$, then find focal length of objective lens and eyepiece.

Answer 1

For astronomical telescope,
We known that, linear magnification.
$m=\frac{f_o}{f_e}$
But Here,
$m=15$
$15=\frac{f_o}{f_e}$
$15f_e=f_o$ ......(1)
The lengths of astronomical telescope, L$=80$cm
We know that, $L=f_o+f_e$ .......(2)
From equation (1) and (2)
$80=15f_o+f_e$
$80=16f_e$

$f_e=5cm$

$f_o=15\times 5$

$f_e=75cm$

$f_o$ and $f_e$ are $75$ and $5$ respectively.