A Galilean telescope of `10`-fold magnification has the length of `45 cm` when adjusted to infinity. Determine :
(a) the focal lengths of the telescope's objective and ocular,
(b) by what distance the ocualr should be displaced to adjust the telescope to the distance of `50 m.`

Explanation

Angular magnification for Galilean telescope in normal adjustment is given as:
`T = f_(0)//f_(e)`
or, `10 = f_(0)//f_(e)` or `f_(0) = 10f_(e)` (1)
The langth of the telescope in this case.
`l = f_(0) - f_(e) = 45 cm`. given,
So, using (1), we get
`f_(e) =+ 5` and `f_(0) = + 50 cm`.
(b) Using lens formula for the objective,
`(1)/(s'_(0)) - (1)/(s_(0)) = (1)/(f_(0))` or, `s'_(0) = (s_(0)f_(0))/(s_(0) + f_(0)) = 50.5 cm`
From the figure, it is clear that,
`s'_(0) = l' + f_(0)` where `i'` is the new tube length.
or, `l' = v_(0) - f_(e) = 50.5 - 5 = 45.5 cm`.
`Delta l = l' - l = 45.5 -45 = 0.5 cm`